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TEANSITS or VENUS. 



t) 



FLATE L 
PATHS OF VENUS 

(MOST NORTHERLY, CENTRAL, AND MOST SOUTHERLY) 

ACROSS THE SUN'S FACE 




R. A. Proctor del. 

DURING THE TRANSITS OF 
A.D. 1631, 1639, 1761, 1769, 1874, 1882, 2004, axd 2012. 

(The region's where the ingress i, the egress e, or the whole transit could be seen, are 
shown in the eight coloured Plates II. — IX.) 



TEANSIT8 OF VENUS, 

A POPULAE ACCOUXT 

OF 

PAST AND COMING TEANSITS 



FROM THE FIRST OBSERVED BY HORROCKS A.D. 1639 
TO THE TRANSIT OF A.D. 2012. 

RICHAED AT PROCTOE, B.A. Camb, 

AUTHOR OF 'SATUSX' * THE SUN' 'OTHER WORLDS THAN OURS ' ETC. 



«' 



A spot like "^iiicli 
Astronomesr in tlie Sun's lucent orb 
Through his glazed optic tube yet never saw, 

MlLTOX 

Et vera ineessu patnit Dea. 

Virgil. 



WITH 20 PLATES (12 COLOURED) A?gD 37 WOODCUTS- 



E. WOETHINGTON AND CO. 

750 BROADWAY, 

NEW YORK. 

1875. 



■X 



<0 



\ 



PEEFACE. 



This work is intended to be partly historical and 
partly explanatory. So far as I know, no book has 
hitherto been published in England giving a com- 
plete account of the transits of 1639, 1761, and 1769, 
and of the various interesting circumstances connected 
with them. This want I have endeavoured here to 
meet, illustrating by maps the conditions under which 
those transits were observed. In the chapters re- 
lating to the transits of 1761 and 1769, I sketch 
the causes of the partial failure of the observations 
then made, and give an account of the attempts made 
in recent years to reconcile those observations with 
the present estimate of the sun's distance. It will be 
observed that in dealing with the latest of these at- 
tempts I adopt the opinion of Continental and American 
astronomers, no longer regarding that attempt as in 
any sense removing the difficulties recognised before 
it was made. 

In Chapter IV. I have given a simple account of 



Ti PREFACE, 

the principles on Avhich the recurrence and observa- 
tion of transits depend. 

In the last chapter I carry on the history of the 
subject to the present time. It would be impossible, 
as Sir Edmund Beckett points out in the latest edition 
of his fine work ' Astronomy without Mathematics/ to 
present the subject adequately without a short account 
of the occurrences of 1869 and 1873 — now belonging 
to the history of transits, and instructive in many 
respects, has It seemed to me best to quote the 
original papers of 1868 and 1869, and then briefly 
sketch the progress of events which led to the arrange- 
ments finally adopted. 

The plans of the various scientific nations for 
the transit now at hand are worthy of the occa- 
sion. Astronomers attach just value to the beautiful 
method of Delisle, while not losing sight of the 
favourable opportunity presented for applying the 
simple method invented by Halley. They have 
wisely noted the fact that all the best Halleyan 
stations are excellent also for Delisle's method, and 
have taken such measures, that if bad weather should 
prevent the beginning or end from being both ob- 
served, one or other may still be utilised. In this 
way new Delislean stations have been obtained by 
the very arrangements which provided for the em- 



PREFACE. Til 

ployment of Halley's method ; and thus the chance 
of absokite failure through bad weather has been very 
largely diminished. The long-neglected region in North 
India has been occupied^ and useful observations will 
doubtless be made there. Southern observing-stations 
are also now amply provided for — first-class Halleyan 
stations having been quadrupled in number since last 
year^ when it was pointed out that the want of them 
endangered the whole scheme of operations. 

The suggested Antarctic expeditions for viewing 
the transit of 1882 have been very properly aban- 
doned. 

A brief account is given at the end of Chapter V. 
of the conditions of the transits of 2004 and 2012. 

Richard A. Proctor. 

London: October 1^14:, 

For the use of Plates X., XL, XII., XIII., and 
XIV., I have to thank the Editor of the ^ Astro- 
nomical Register,' Rev. S. J. Jackson. These pic- 
tures originally appeared in the ' Illustrated London 
News,' for which journal I drew them. Electros 
were supplied to Mr. Jackson for use in the ^ Re- 
gister,' and were lent to me by him. These plates 
have also appeared, slightly reduced by some process 
unknown to me, in the Xew York ' Daily Graphic' 



CONTENTS. 



CHAPTER PAGE 

I. Transits of the Setenteenth Centurt .... 1 

II. The Transit of 1761 . . . . . . . 27 

III. The Transit of 1769 67 

IV. Of Transits and their Conditions . . . .93 
V. The Coming Transits ' . .156 



TABLE 

I. Transit of 1874. Places foe obserting early be- 
ginning . . 235 

11. Transit of 1874. Places fob obserting late be- 
ginning ib. 

III. Transit of 1874. Places for observing early ending 236 

lY. Transit of 1874. Places for obserting eate ending ib. 

V. Transit of 1874. Places for observing greatest and 

EEAST duration . . . . . . .237 

VI. For determining the Sun's distance corresponding 

TO ANY GIVEN PARALEAX .238 



ILLUSTEATIONS. 



PLATES. 

PLATE 

K I. Chords of transit in 1631, 1639, 1761, 1769, 1874, 1882, 

2004, and 2112 Frontispiece. 

PAGE 

II.i Chart of the transit of 1631 -^ To face each other j- 12 

III. ., „ 1639 J between pages I 13 

IV. „ ' ., ^ 1761 1 
V. „ „ 1769 / 



VI. 
VII. 



1874 1 

1882 / 

2004 "1 

2012 J 



{ 


46 
47 


{ 


92 
93 


r 


92 


I 


93 



VIII. 
IX. „ „ 201 

^ X. Illustrating passage of Venns's shadow-eone over earth 

in 1631, 1639, 1874, and 1882. . To face page 119 

•^XI. Transit-chords, &c., in 1874 and 1882 . . „ 125 



^ Plates II.— IX., and Plates XVII., XVIII., are to be arranged 
so that all the titles, TEAXSIT OF 1631, 1639, &c., lie towards 
the left when the book is opened between any pair of plates and held 
in the usual manner. Plate XX. is to read the other way ; that is. 
it is to have its title, Plate XX., towards the right. 



Xll 



ILLUSTRATIONS. 



/.a, 



PLAT'S 
- XII. 

XIII. 

XIV. 
^ XY. 

L. XVI. 

XVII. 
XVIII. 

XIX. 



Sun-yiew of the Eartli at beginning 

of transit of 187 J: 

Sun-view of the Earth at end of 

transit of 1874:, 

Sun-view of the Earth at beginning 

of transit of 1882 

Sun-view of the Earth at end of 

transit of 1882 



To face each other r 126 
between jpages 1 1 2 7 



ri26 
1 127 



The Earth's passage through Venus's shadow-cone during 
the transit of 1874 .... To face page l^o 



end 



■y 



between pages \ 1 4 7 



Paths of Venus's centre across Sun's disc, as seen from 
twelve stations, in 1874 . . . To face page \b\ 



t-' XX. The same in miniature, shown on the Sun's disc 



152 



WOODCUTS IN TEXT. 



1. Paths of Venus and the Earth 

2. Transit of 1639, as observed by Horrocks 

3. „ 1761. as computed by Halley, and as observed 

4. Illustrating conditions of same, as computed by Halley 
0. Projection of same on Halley's mistaken assumption 

6. Three views of ' black drop '...... 



PAGE 

2 
21 
37 
38 
3^ 
57 



ILLUSTBATIOXS. 



xiu 



7. Venus distorted {Mai/er) 

8. The ' black drop ' as seen by Bajley 

9. „ „ Hirst .... 
'lO. ,, „ Bevis 

11 and 12. Explaining formation of 'black drop' 

] 3. Illustrating determination of Sun's distance by transit obser^ 
vations ... r .... . 



14-. Illustrating effects of Earth's rotation on Venus in transit 

15. Conjunctions of Earth and Venus 

16. Showing transit-regions of Earth's orbit .... 

17. Illustrating occurrence of transits 

18. Regression of conjunction-lines over transit-regions . 



19. Position of conjunction-lines in years 1870, 1871, 1873. 187^. 
and 1876 



20. Venus's shadow-cone 

21, 22, 23, 24, 25, and 26 fall in Plate X. 



PAGE 

61 
62 
63 
63 
64 

94 
98 
102 
106 
107 
110 



115 

118 

facing 119 



27, 28, 29, 30, and 31. Illustrating passage of Venus's shadow-cone 
over Earth in 1761, 1769. 2004, and 2012. 

32. Showing Halleyan poles midway between Delislean poles . 

33. Illustrating case unfavourable for Halley's method 

34. ,5 interaal and external shadow-cones 

35. Internal and external shadow-cones .... 

36. Explaining Plate XVI 

37. Illustrating construction of Plate XIX 

38. Transit of 1882, incrress 



124 
131 
135 
140 
142 
145 
148 
154 



XIV ILLUSTRATIONS. 

FIG. PAGE 

39. Transit of 1882, egress . - 155 

40. Effect of rotation on progress of a tiansit 158 

41. ,, position of transit-chords 159 

42. Illustrating the photographic and direct method . . . 208 

43. „ „ „ ... 209 



TRANSITS OF VENUS. 

CHAPTER I. 

TB Ay SITS OF THE SEVENTEENTH CENTURY. 

As soon as the Copernican theory of the solar system 
was established, astronomers perceived that the inferior 
planets^ Mercury and Yenus^ must from time to time 
appear to cross the face of the sun. For although on 
most of these occasions when either planet passes 
between the sun and the earth, no transit was to be 
expected, the planet either passing above or below the 
face of the sun, yet it could not but happen that, in 
the course of many such conjunctions, the planet 
would make a passage at so small a distance north or 
south of the sun's centre as to appear for a time to be 
u|)on the sun's disc. To make this clear, without 
entering into any nice details at this stage, let e e and 
Yv (fig. 1) be the paths of the Earth and Venus, 



2 TRANSITS OF VENUS. 

respectively^ around the Sun^ s.^ Then if we suppose^ 
the path e e to lie in the level of the paper^ we must 
imagine one-half of the path v v — the half Y^ v v^ — to 
lie above the level of the paper^ the other half, v y y% 
lying below that level — not greatly above or below ; 
in fact^ the short white lines near v and Y show how 
much these parts of the path of Venus are to be 
supposed respectively above and below the level of 
the paper. btill^ it will be clear that when Venus is^ 




Fig. 1. — Showing the paths of Venus and the Earth, and indicating 
their inclination and the line of intersection of their planes. 

as at v, between the Sun and the Earth at s and e^ she 
is not really on the line s E, but considerably below 
it ; and, as supposed to be seen from the Earth, she 
passes below the Sun. When in conjunction on the 
other side of v^ v\ Venus passes above the Sun. Only 
when she is in conjunction nearly at v^ (the Earth 
near E^), or nearly at v^ (the Earth near /), will she 

^ E is supposed to be the place occupied by the earth at the time of 
the autumnal equinox. 



TBAXSITS OF THE SEVENTEENTH CENTURY, 3 

appear to cross the face of the Sun. But in the course 
of many conjunctions there must be some which take 
place when the two planets are thus placed; that is, 
either near Y^ and E^, or near v and e\ Similar 
remarks apply to the case of Mercury. 

This was early perceived by the followers of 
Copernicus. The Ptolemaic system did not. indeed, 
preclude the possibility of such phenomena as transits ; 
but since the older astronomers regarded the planets as 
shining by their own inherent lustre, it was not to be 
expected that, even if a transit occurred, the planet 
would be discernible while crossino; the sun's face. 
And as in reality the Ptolemaic system gave no means 
of inferring the relative distances of the several planets 
(including the sun^), there could not even be any 
certain assurance that Venus or Mercury ever came 
between the earth and the sun. It was only by a 
mere assumption that the old astronomy assigned to 
the sun a sphere outside the spheres of Mercury and 
Venus. 

Still we find that, even so far back as the ninth 
century, Mercury was supposed to have been seen as 
a dark spot on the face of the sun. Doubtless one of 
those large sun-spots, which from time to time are 
visible to the naked eye, had attracted attention, and 
was regarded by the ignorant as caused by the passage 
of one or other of the planets. Mercury or Venus, 
between the earth and the sun. Venus being probably 

* The sun and moon were ' planets ' in tlie old astronomy ; and we 
still find traces of the nsage in some modern expressions. 

B 2 



4 TRANSITS OF VENUS. 

conspicuous at the time, either as a morning or evening 
star, the less familiar planet Mercury afforded a con- 
venient explanation of the dark spot. The account 
of the phenomenon accords well with the belief that a 
solar spot was seen, for we are told by the author of 
the • Life of Charlemagne ' that Mercury was visible 
as a black spot upon the sun for eight consecutive 
days in April of the year 807. Kepler, who was 
perfectly well aware that Mercury moves too rapidly 
to remain even for as many hours on the sun's disc, 
endeavoured to show that the expression originally 
used in the manuscript had not been octo dies, but 
octoties, a barbaric form of octies, for ^ eight times.' 

It is now well known that Mercury is far too 
small to be seen by the naked eye when crossing the 
sun's disc. And this fact disposes of the statement 
made by the famous physician Ebn Roschd (commonly 
called Averroes), in his Ptolemaic Paraphrase, to the 
effect that he saw the planet on the sun in the year 
1161, at a time Avhen Mercury really was in inferior 
conjunction. AYe need not, however, question the 
veracity of the learned doctor, seeing that Kepler him« 
self supposed he had seen the planet upon the sun on 
one occasion. When, a few years later, the existence 
of sun-spots was detected by the telescope, Kepler 
admitted that in all probability he had seen such a 
spot, and not the planet Mercury. 

After Kepler had completed his Rudolphine tables 
of the planetary motions he was able to arrive at 
tolerably accurate results as to the epochs of the 



TRANSITS OF THE SEVEXTJEENTH CEXTURY, 5 

transits of Mercury and Yenus over the solar disc. 
In fact^ he announced, in 16275 that in the year 1631 
both Mercury and Venus would pass over the sun's 
face — Mercury on Xovember 7, and Yenus on De- 
cember 6 ; and that in 1761 Yenus would again pass 
across the face of the sun. 

As the first occasion on which the transit of an 
inferior planet was ever witnessed, the transit of 
Mercury in 1631 has an interest resembling that which 
attaches to the first observation of a transit of Yenus, 
eight years later. Therefore I think the reader will 
be interested to hear how Cxassendi succeeded in ob- 
serving Mercury in transit. 

Gassendi made preparations for the observation of 
the transit at Paris. The manner in which he ob- 
served the phenomenon was somewhat remarkable. 
Through a small aperture in a shutter the solar light 
was admitted into a darkened room, and an image of 
the sun, some nine or ten inches in diameter, was 
formed upon a white screen. A carefully divided 
circle was traced upon this screen, and the whole was 
so arranged that the image of the sun could be made 
to coincide exactly with the circle. As Gassendi was 
anxious to ascertain the exact moment of the ingress 
of the planet upon the sun's disc, or-^supposing he 
should fail in that respect — at least to determine the 
moment of egress, and as he had no trustworthy clock, 
he determined that the altitude of the sun should be 
carefully estimated several times during the progress 
of the transit, and particularly at the moment of 



6 TRANSITS OF VENUS. 

egress. It was necessary, therefore, that he should 
have an assistant, and, further, that his assistant should 
work in another room ; for from the room in which 
Gassendi was working the sun's light, as I have said, 
had been carefully excluded, save at the minute 
aperture in the window-shutter. Accordingly, Gassendi 
placed his assistant in a room above him, with a large 
quadrant for taking altitudes, instructing him to ob- 
serve the height of the sun as soon as he heard 
Gassendi stamp upon the floor of the room beneath. 
A clumsy arrangement, truly, when compared with 
the subtle devices of modern astronomers — with the 
aid which they derive from powerful telescopes, all but 
perfect clocks, and, where need arises for communi- 
cating with one another from distant stations, the 
instantaneous indications of telegraphy. Yet we can- 
not but admire the spirit in which Gassendi worked, 
the readiness with which, for want of more perfect 
instruments^ he set himself to invent arrangements 
which suited his requirements, and the skill Avith 
which he availed himself of those imperfect adap- 
tations. 

And if we admire these qualities in Gassendi, still 
more must we admire the patience with which he 
waited for the commencement of the phenomenon. 
Modern astronomy is able to announce, within three 
or four minutes, the instant at which a transit will 
commence at any given spot upon the earth's surface. 
But Kepler's prediction respecting Mercury's motions 
did not layxilaim to any accuracy of this sort. So 



TI^AXSITS OF THE SEVEXTEEXTH CEXTURY, / 

uncertain did the epoch of the occurrence appear to 
be, that Gassendi began to watch for the transit 
two days before the date assigned by Kepler for its 
occurrence. 

The 5th of November proved unfavourable for 
observation, the day being rainy. The next day was 
also unsuitable, clouds having overspread the sky 
durino; nearlv the whole dav. The mornino^ of the 7th. 
the day appointed by Kepler for the transit, was also 
cloudy. Thus Gassendi began his watch on that day 
with the uncomfortable feeling that during some part 
of the two preceding days the planet might already 
have passed over the sun's disc, — perhaps that the 
transit had been completed but a few minutes before 
the clouds broke up on the morning of the 7th. 

A little before eight the sun shone for a few 
minutes through the openings between the clouds, but 
there still remained enough mist to prevent Gassendi 
from being able to determine whether any spot existed 
upon the image of the sun in his observing-room. 
Xearly an hour passed before the sun was sufficiently 
clear of clouds to enable Gassendi to make any satis- 
factory observations. Towards nine, however, the 
sun became distinctly visible, and turning to the image 
on the screen, the astronomer perceived upon it a 
small black spot. He could not believe, however, that 
this was Mercury, as the received estimate of the 
planet's dimensions had led him to look for a spot 
nearly twice as large. As he was familiar with the 
nature of solar spots, and the rapid manner in which 



8 TRANSITS OF VE2s'US. 

they form, he concluded that one had made its appear- 
ance on the sun's surface since the preceding day. 
At nine o'clock he had another opportunity of observ- 
ing the spot^ and he carefully estimated its position, 
intending to make use of it as a point of reference for 
determining the path of the planet in transit, if 
he should be fortunate enough to witness that phe- 
nomenon. Soon after, he had another view of the 
spot, and was surprised to find that it had moved away 
considerably from its former position. He felt assured 
that no ordinary solar spot could have moved so 
rapidly; but still he could not persuade himself that 
he was looking at Mercury in transit, having so fully 
satisfied his mind respecting the dimensions which the 
planet would exhibit. Besides, the hour had not yet 
arrived at which Kepler had predicted that the transit 
would begin. 

Gassendi was still in doubt, and endeavouring to 
recall the circumstances of his former measurement, 
in order to convince himself that he had made no 
mistake, when the sun again made his appearance 
through the clouds, and it was apparent that the spot 
had moved yet farther from its original place. Xo 
room now remained for doubt. It was clear that the 
phenomenon which had been so long and so anxiously 
awaited by the astronomer was already in progress. 
He immediately stamped upon the floor to attract the 
notice of his assistant. But this person, whose name 
has not reached us, was possessed of less patience than 
Gassendi. He probably felt much less interest in the 



TJRANSITS OF THE SEVENTEENTH CENTURY. 9 

phenomenon ; possibly^ he placed very little faith in 
the calculations of Kepler. Whatever was the reason, 
he had grown weary of watching, and had left his 
post. Gassendi had to continue his observations 
alone, hoping that at least his {assistant would re- 
turn before the planet had passed completely off the 
sun's face. Fortunately this happened ; the requisite 
observations were made for determining the time of 
egress ; and thus an important addition was made to 
our knowledge of the motions of the innermost planet 
of the solar system. 

Gassendi sent an amusing account of his observa- 
tions to Professor Shickhard, of the University of 
Tubingen. ^ The crafty god,' he wrote, ^ had sought 
to deceive astronomers by passing over the sun a little 
earlier than was expected, and had drawn a veil of 
dark clouds over the earth in order to make his escape 
more effectual. But Apollo, acquainted with his 
knavish tricks from his infancy, would not allow him 
to pass altogether unnoticed. To be brief, I have 
been more fortunate than those hunters after Mercury 
who sought the cunning god in the sun. I found him 
out, and saw him where no one else had hitherto seen 
him.' He states that the planet, as seen projected on 
the image of the sun, did not appear altogether black, 
but was greyish, and somewhat ruddy round the 
margin. Doubtless these peculiarities were due to the 
method of observation employed by the astronomer. 
He estimated the apparent diameter of the spot at 
about one-ninetieth part of the sun's apparent diameter. 



lO TRANSITS OF VENUS, 

an estimate considerably exceeding the true dimen- 
sions, but still more considerably below the dimensions 
which astronomers had been disposed to assign to the 
planet. 

Gassendi, although he did not observe the com- 
mencement of the transit, was yet able to compute 
the time of its occurrence. He found that the transit 
had begun nearly five hours before the time assigned 
by Kepler.^ 

I have mentioned that Kepler had predicted that 
a transit of Venus would take place on December 6, 
1631. It need hardly be said that Gassendi, after his 

^ The second observed transit of Mercury took place on November 3, 
1651. The observations of Gassendi had enabled astronomers to esti- 
mate the epoch of the transit much more exactly than in the former 
instance. It resulted from their calculations that the phenomenon 
would not be visible in England, or indeed in Europe ; but would be 
well seen over a large part of Asia. Accordingly a young Englishman, 
Jeremiah Shakerley, went to Surat, in India, for the purpose of witness- 
ing the phenomenon. Such a journey undertaken for such a purpose in 
an age when sea-voyages were not only much more protracted, but also far 
more dangerous than in the present day, must be looked upon as a re- 
markable and commendable instance of devotion to scientific pursuits. 
It is pleasing to be able to record that the energy of the young English- 
man was rewarded by complete success. 

The third observed transit took place on May 3, 1661. It was 
observed by Hevelius at Dantzic, and at London by Huyghens, Street, 
and Mercator. Hevelius was surprised to find that the diameter of the 
planet was very much smaller than he had been led to expect. He 
found on measurement that Gassendi's estimate was nearly twice as 
great as the true diameter of the planet. 

The fourth transit of Mercury was observed by Halley at St. Helena 
on November 7, 1677. He was the first astronomer who had ever 
observed the complete passage of the planet across the solar disc. 

Later transits of Mercury have no special historical interest, though 
observations of considerable importance were made during the transits 
of 1736, 1799, and 1868. 



TIlA^SITS OF THE SEVENTEESTR CENTURY, II 

success in observing the transit of IMercury^ had 
good hopes of observing Venus to even greater ad- 
vantage. It is true that, according to Kepler's calcu- 
lation^ the transit might be expected to begin only 
towards sunset^ and it was therefore possible that the 
phenomenon would not be visible at all in Europe. 
But it was equally possible that any error in the 
calculation might lie in the other direction, and so 
the whole transit be favourably seen before sunset. 
Gassendi took the same measures for observing the 
transit as in the case of Mercury. He had proposed 
to observe the sun on December 4 and 5, but ^ an 
impetuous storm of wind and rain rendered the face of 
the heavens invisible on both those days. On the 6th 
he continued to obtain occasional glimpses of the sun 
till a little past three o'clock in the afternoon, but no 
indication of the planet could be discerned upon the 
sun's disc as depicted upon the white circle. On the 
7th he saw the sun during the whole forenoon, but he 
looked in vain for any trace of the planet.' ^ It is 
now well known,' proceeds Prof. Grant, from whose 
account I have just quoted, ^that the transit of the 
planet took place during the night between December 
6 and 7.' I do not know where any calculation of the 
circumstances of the transit can be found ; but an 
investigation of my own (sufficiently accurate for a 
past and unseen phenomenon) shows that in the South- 
eastern parts of Europe the egress might have been 
observed, occurring for those parts after sunrise on the 



12 TRANSITS OF VENUS. 

morning of December 7.^ Plate II. shows the parts 
of the earth whence the transit might have been seen 
wholly or in part. The position of the line C D, which, 
accordmg to my calculation, marks the boundary be- 
tween the places where day and night were in progress 
in the Northern hemisphere at egress, shows the parts 
of Europe whence the end of the transit might have 
been observed. 

Kepler had stated that after the transit of 1631 
there would be none till the year 1761. According 
to his calculations, Venus, when in her inferior con- 
junction on December 4, 1639, would pass very near 
to the sun's centre, but not quite near enough for a 
transit to occur, the planet passing beloic — that is, 
south of the sun. On the other hand, the tables of 
Lansberg, a Belgian astronomer, who followed the old 
system of computation, seemed to show that Venus 
would on this occasion transit the upper or northern 
part of the sun's face. Horrocks, a young and then 
unknown astronomer, having been led to examine the 
tables of Venus, found that though Kepler's were much 
more exact than Lansberg's, a transit would really 
occur, Venus passing below the centre of the sun, as 
Kepler had predicted, but not so low as to miss the 

^ M. Dubois, in his admirable work, ' Les Passages de Venns,' gives 
the foUoTiing hnmoroiis explanation of Gassendi's failure : — ' Le Pas- 
sage de Yenus, qui sans doute n'etait pas predit avec line precision 
suffisante, ne fut pas observe — ^Vi^orcZparceqiie Gassendi, qui sappretait 
a robservation, en fiit enipeche par la plnie, mais surtout parce que le 
passage eiit lien pendant la niiit poiir les observateiirs europeens.' [The 
italics are mine.] 




"Ci\ o) 





^ 2 

^ -^ 






33 



<o 



THAXSITS OF THE SEVESTEEyTH CEXTVRY, I 3 

sun's disc altogether. The circumstances under which 
Horrocks made this discovery possess considerable 
interest, and I propose to devote some space to his 
account of them. 

While preparing himself for practical observation, 
Horrocks undertook (apparently from sheer love of 
science) the computation of Venus's motions from the 
tables of Lansberg. These tables were so highly 
valued by their author that he had spoken of them 
as superior to all others, quantum lenta solent inter 
viburna cupressi. But Horrocks recognised many im- 
])erfections in them, and at length, as he says, ' broke 
off the useless computation, resolved for the future 
with his own eyes to observe the positions of the stars 
in the heavens ; but, lest so many hours should be 
entirely thrown away,' he made use of his results to 
predict the positions of the planets. ' While thus 
engaged, I received,' he proceeds, ' my first intimation 
of the remarkable conjunction of Venus and the sun ; 
and I regard it as a very fortunate occurrence, inasmuch 
as about the beginning of October it induced me, in 
expectation of so grand a spectacle, to observe with 
increased attention.' Nevertheless, his heart w^as 
wroth within him against Lansberg, insomuch that he 
could not refrain from the extreme step of ' forgiving ' 
him in the following agreeable terms : ' I pardon, in 
the meantime, the miserable arrogance of the Belgian 
astronomer who has overloaded his useless tables with 
such unmerited praise, and cease to lament the mis- 
application of my own time, deeming it a sufficient 



14 TRANSITS OF VENUS. 

reward that I was thereby led to consider and to fore- 
see the appearance of Venus in the sun. But, on the 
other hand, may Lansberg forgive me' (this is charming) 
' that I hesitated to trust him in an observation of such 
importance, and from having been so often deceived by 
his pretensions to universal accuracy that I disregarded 
the general reception of his tables.' ' Lest a vain 
exultation should deceive me,' he proceeds, ' and to 
prevent the chance of disappointment, I not only de- 
termined diligently to watch the important spectacle 
myself, but exhorted others whom I knew to be fond 
of astronomy to follow my example; in order that the 
testimony of several persons, if it should so happen, 
might the more effectually promote the attainment of 
truth, and because by observing in different places our 
purpose would be less likely to be defeated by the 
accidental interposition of clouds, or any fortuitous 
impediment.' He was particularly anxious, because 
Jupiter and Mercury seemed by their positions to 
threaten bad weather. ^ For,' says he, ^ in such ap- 
prehension I coincide with the opinion of the astrologers, 
because it is confirmed by experience ; but in other 
respects I cannot help despising their puerile vanities.' 
Among the astronomers to whom he wrote was his 
friend Crab tree. ^ 

^ Both these ardent students of astronomy died young. Horrox 
(or Horrocks, as his name is now more commonly spelt) was but twenty 
years old when he calculated the transit, so that his feat may not in- 
aptly be compared to that of Adams in calculating the place of the 
unknown planet Neptune within a few months of taking his degree. 
Each instance of an early mastery of difficult problems was fated to 



THAXSITS OF THE SEVENTEENTH CENTURY. I 5 

In Avhat follows I quote the account given by 
Horrocks himself of the observations made upon this 
occasion, using the translation given by the Rev. Mr. 
Whatton.^ 

^Following the example of Gassendi/ says Horrocks, 
^ I have drawn up an account of this extraordinary 
sight, trusting that it will not prove less pleasing to 
astronomers to contemplate Venus than Mercury, 
though she be wrapt in the close embraces of the sun : 

Vinclisqiie nova ratione paratis 
Admisisse Deos. 

Hail ! then, ye eyes that penetrate the inmost recesses 
of the heavens, and, gazing upon the bosom of the sun 
with your sight-assisting tube, have dared to point out 
the spots on that eternal luminary ! And thou, too, 
illustrious Gassendi above all others, hail ! thou who, 
first and only, didst depict Hermes' changeful orb in 
hidden congress Avith the sun. Well hast thou re- 
stored the fallen credit of our ancestors, and triumphed 
o'er the inconstant wanderer. Behold thyself, thrice 
celebrated man! associated with me, if I may venture 
so to speak, in a like good fortune. Contemplate, I 
repeat, this most extraordinary phenomenon, never in 



meet with neglect ; but Horrocks died before justice had been done him. 
Adams was quickly able to prove that bis work was sound, notA\dth- 
standing the coolness with which it had been received by official 
astronomers. Horrocks died in 1641, in his twenty-second year. Crab- 
tree is supposed to have been killed at the battle of Naseby Field. 

^ The memoir accompanying Mr. Whatton's translation will be 
found full of interest. The complete work is published by Macintosh, 
24 Paternoster Kow. 



1 6 TRANSITS OF VENUS. 

our time to be seen again ! the planet Venus, drawn 
from her seclusion, modestly delineating on the sun, 
without disguise, her real magnitude, whilst her disc, 
at other times so lovely, is here obscured in melancholy 
gloom ; in short, constrained to reveal to us those 
important truths, which Mercury on a former occasion 
confided to thee. 

^ How admirably are the destinies appointed ! 
How wisely have the decrees of Providence ordered 
the several purposes of their creation ! Thou, a 
profound divine, hast honoured the patron of wisdom 
and learning ; whilst I, whose youthful days are scarce 
complete, have chosen for my theme the queen of love, 
veiled by the shqde of Phoebus' light. 

' Whilst I was meditating in what manner I should 
commence my observation of the planet Venus, so 
as effectually to realise my expectations, the recent 
and admirable invention of the telescope afforded me 
the greatest delight, on account of its singular ex- 
cellence and superior accuracy above all other instru- 
ments. For although the method which Kepler 
recommends in his treatise on C)ptics, of observing 
the diameter and eclipse of the sun through a plain 
aperture without the aid of glasses, is very ingenious, 
and in his opinion, on account of its freedom from 
refraction, preferable to the telescope ; yet I was un- 
able to make use of it, even if I had wished to do so, 
inasmuch as it does not show the sun's image exactly, 
nor with sufficient distinctness, unless the distance 
IVom the aperture be very great, which the smallness 



TBAXSITS OF THE SEVEXTEEXTH CEXTURY. 1 7 

of my apartment would not allow. Moreover, I was 
afraid to risk the chance of losing the observation ; 
a misfortune which happened to Schickard and 
Mostling, the astronomer to the Prince of Ilesse^ as 
Gassendi tells us in his " Mercury : " for they, expect- 
ing to find the diameter of Mercury greater* than it 
was reasonable to anticipate, made use of so large an 
aperture that it was impossible to distinguish the 
planet at all, as Schickard himself has clearly proved ; 
and even though Venus gave promise of a larger 
diameter, and thereby in some measure lessened this 
apprehension, and 1 was able to adapt the aperture to 
my own convenience, yet in an observation that could 
never be repeated I preferred encountering groundless 
fears to the certainty of disappointment. Besides, 1 
possessed a telescope of my own, of such power as to 
show even the smallest spots upon the sun, and to 
enable me to make the most accurate division of his 
disc ; one which, in all my observations, I have found 
to represent objects with the greatest truth. 

' This kind of instrument, therefore, I consider 
ought always to be preferred in such experiments. 

' Having attentively examined Venus with my 
instrument, I described on a sheet of paper a circle 
Avhose diameter was nearly equal to six inches, 
the narrowness of the apartment not permitting me 
conveniently to use a larger size. This, however, 
admitted of a sufficiently accurate division ; nor could 
the arc of a quadrant be apportioned more exactly, 
even with a radius of fifty feet, which is as great a 



1 8 TRANSITS OF VENUS. 

one as any astronomer has divided; and it is in my 
opinion far more convenient than a larger, for although 
it represents the sun's image less, yet it depicts it more 
clearly and steadily. I divided the circumference of 
this circle into 360° in the usual manner, and its 
diameter into thirty equal parts, which gives about as 
many minutes as are equivalent to the sun's apparent 
diameter ; each of these thirty parts was again divided 
into four equal portions, making in all 120 ; and these, 
if necessary, may be more minutely subdivided ; the 
rest I left to ocular computation, which, in such small 
sections, is quite as certain as any mechanical division. 
Suppose, then, each of these thirty parts to be divided 
into 60'', according to the practice of astronomers. 
AYhen the time of the observation approached I re- 
tired to my apartment, and having closed the windows 
against the light, I directed my telescope, previously 
adjusted to a focus, through the aperture towards the 
sun and received his rays at right angles upon the 
paper already mentioned. The sun's image exactly 
filled the circle, and I watched carefully and unceasingly 
for any dark body that might enter upon the disc of 
light. 

' Although the corrected computation of Venus's 
motions which I had before prepared, and on the 
accuracy of which I implicitly relied, forbade me to 
expect anything before three o'clock in the afternoon 
of the 24th ; yet since, according to the calculations of 
most astronomers, the conjunction should take place 
sooner— by some even on the 23rd— I was unwilling to 



TRAXSITS OF THE SEVENTEEXTH CENTURY. 1 9 

depend entirely on my own opinion^ which was not suffi- 
ciently confirmed^ lest by too much self-confidence I 
might endanger the observation. Anxiously intent, 
therefore, on the undertaking through the greater part 
of the 23rd^ and the whole of the 24th, I omitted no 
available opportunity of observing her ingress. I 
watched carefully on the 24th from sunrise to nine 
o'clock, and from a little before ten until noon, and at 
one in the afternoon, — being called away in the in- 
tervals by business of the highest importance, wdiich for 
these ornamental pursuits I could not wdth propriety 
neo-lect.^ But durino* all this time I saw nothino; in the 
sun except a small and common spot, consisting as it 
were of three points at a distance from the centre 
towards the left, which I noticed on the preceding and 
following days. This evidently had nothing to do 
with Venus. About fifteen minutes past three in the 
afternoon, when I was again at liberty to continue my 
labours, the clouds, as if by Divine interposition, were 
entirely ^dispersed, and I was once more incited to the 

^ Presumably, as JVIr. Whatton points out,^ 'the business of the 
highest importance ' here referred to was the duty of conducting divine 
service, as November 24, Old Style, was a Sunday. Mr. Whatton quotes 
the following passage from one of Thomas Hearne's pocket-books, dated 
February 8, 1723: 'Mr. Horrox, a young man, minister of Hoole, a 
very poor pittance, within four miles of Preston, in Lancashire, was a 
prodigy for his skill in astrojiomy, and had he lived, in all probability 
he would have proved the greatest man in the whole world in his 
profession. He had a very strange unaccountable genius, and he is 
mentioned ^A\h great honour by Hevelius upon account of his discovery 
of Venus in the sun, upon a Sunday ; but being called away to his 
devotions and duty at church, he could not make such observations as 
otherwise he would have done.' 

c 2 



20 TRANSITS OF VENUS, 

grateful task of repeating my observations. I then 
beheld a most agreeable spectacle, the object of my 
sanguine wishes, a spot of unusual magnitude and 
of a perfectly circular shape, which had already fully 
entered upon the sun's disc on the left, so that the 
limbs of the sun and Venus precisely coincided, 
forming an angle of contact. Xot doubting that this 
was really the shadow of the planet, I immediately 
applied myself sedulously to observe it. 

' In the first place, with respect to the inclination, 
the line of the diameter of the circle being perpen- 
dicular to the horizon, although its plane was somewhat 
inclined on account of the sun's altitude, I found that 
the shadow of Venus at the aforesaid hour — namely, 
fifteen minutes past three — had entered the sun's disc 
about 62° 30', certainly between 60° and 63°, from 
the top towards the right. This was the appearance 
in the dark apartment ; therefore out of doors beneath 
the open sky, according to the laws of optics, the 
contrary would be the case, and Venus would be below 
the centre of the sun, distant 62° 30' from the lower 
limb, — or the nadir, as the Arabians term it. The in- 
clination remained to all appearance the same until 
sunset, when the observation was concluded.^ 

' In the second place, the distance between the 
centres of Venus and the sun, I found by three ob- 
servations, to be as follows : — 



^ Horrocks observed Yeniis close by the place marked ^, in Plate I. 
She had barely completed irgress when he first saw her, and when his 
observations closed she had advanced nearl}^ two diameters of herself 



TRANSITS OF THE SEVEyTEEXTH CENTURY. 2i 

Distance 
The Hour of the Centres 

At 3.15 by the clock . . . . . . 14 24" 

„ 3.35 „ 13' 30'' 

„ 3.45 „ 13' 0" 

,, 3.50 tlie apparent sunset. 

The true setting being 3.45^ and the apparent about 
five minutes later^ the difference being caused by 
refraction. The clcck^ therefore, was sufficiently 
correct. 

^ In the third place, I found, after careful and 
repeated observation, that the diameter of Venus, as 
her shadow was depicted on the paper, was larger, 
indeed, than the thirtieth part of the solar diameter, 
though not more so than the sixth, or at the utmost 

along tlie line of transit from the place just noted. His picture is too 
elaborate to be given in full, but the accompanp::g driTTing (fig. 2 ) 




Fig, 2. — The Transit of 1639, as observed by Horrocks. 

serves sufficiently to show what he observed — v being the position of 
Venus when first observed, y' the position she had reached when the 
sun was about to set. 



22 TRANSITS OF VENUS. 

the fifth of such a part. Therefore^ let the diameter 
of the sun be to the diameter of Venus as 30' to V \2'\ 
Certainly her diameter never equalled V 30"", scarcely 
perhaps V 20^\ and this was evident as well when the 
planet was near the sun's limbs as when far distant 
from it. 

' This observation was made in an obscure village, 
where I have loug been in the habit of observing, 
about fifteen miles to the north of Liverpool, the 
latitude of which I believe to be 52° 20', although by 
the common maps it is stated to be 54° 12'; therefore, 
the latitude of the village will be 53° 35', and the 
longitude of both 22° 30' from the Fortunate Islands, 
now called the Canaries. This is 14° 15' to the west 
of Uraniburg, in Denmark, the longitude of which is 
stated by Brahe, a native of the place, to be 36° 45' 
from these islands. 

' This is all I could observe respecting this cele- 
brated conjunction during the short time the sun 
remained in the horizon: for although Venus continued 
on his disc for several hours, she was not visible to me 
for longer than half an hour, on account of his so 
quickly setting. Nevertheless, all the observations 
Avhich could possibly be made in so short a time I 
was enabled by Divine Providence to complete so 
effectually that I could scarcely have wished for a 
more extended period. The inclination was the only 
point upon which I failed to attain the utmost pre- 
cision ; for, owing to the rapid motion of the sun, it 
was difficult to observe with certainty to a single 



TBANSITS OF THB SEVENTEENTH CENTURY. 23 

degree ; and I frankly confess that I neither did nor 
could ascertain it. But all the rest is sufficiently 
accurate, and as exact as I could desire,' 

Horrocks was not the only observer of the transit 
of 1639. ^I had written/ he says, ^to my most 
esteemed friend William Crabtree, a person who has 
few superiors in mathematical learning, inviting him 
to be present at this Uranian banquet, if the weather 
permitted ; and my letter, which arrived in good time, 
found him ready to oblige me. He therefore carefully 
prepared for the observation, in a manner similar to 
that which has been before mentioned. But the sky 
was very unfavourable, being obscured during the 
greater part of the day with thick clouds ; and as he 
was unable to obtain a view of the sun, he despaired 
of making an observation, and resolved to take no 
further trouble in the matter. But a little before 
sunset — namely, about thirty -five minutes past three 
— the sun bursting forth from behind the clouds, he 
at once began to observe, and was gratified by behold- 
ing the pleasing spectacle of Venus upon the sun's 
disc. Rapt in contemplation, he stood for some time 
motionless, scarcely trusting his own senses, through 
excess of joy ; for we astronomers have, as it were, a 
womanish disposition, and are overjoyed with trifles, 
and such small matters as scarcely make an impres- 
sion upon others; a susceptibility which those who 
will may deride with impunity, even in my own 
presence ; and if it gratify them, I too will join in the 
merriment- One thing I request : let no severe Cato 



24 TRANSITS OF VENUS. 

be seriously offended with our follies ; for, to speak 
poetically, what young man on earth would not^ like 
ourselves, fondly admire Venus in conjunction with 
the sun, pulchritudinem divitiis conjunctam ? 

' But to return, he from his ecstacy and I from 
my digression. In a little while the clouds again 
obscured the face of the sun, so that he could observe 
nothing more than that Venus was certainly on the 
disc at the time. What he actually saw in so short 
a space was as follows : In the apartment Venus 
occupied the right side of the sun, being higher than its 
centre, and therefore in the heavens lower, and on the 
left. She was distant at the aforesaid hour — namely, 
thirty-five minutes past three — a sufficiently appre- 
ciable space from the sun's left limb, but Crabtree's 
opportunity was so limited that he was not able to 
observe very minutely either the distance itself or the 
inclination of the planet. As well as he could guess by 
his eye, and to the best of his recollection, he drew 
upon the paper the situation of Venus, which I found 
to differ little or nothing from my own observation ; 
nor indeed did he err more than Apelles himselt 
might have done in so rapid a sketch. He found 
the diameter of Venus to be seven parts, that of the 
sun being 200, which, according to my calculations, 
gives about 1^ 3'^ 

' This observation was made near Manchester, 
called by Antoninus, Mancunium, or Manucium, the 
latitude of which Mr. Crabtree makes 52° 24^ ; and 
the common tables 54° 15^ ; the longitude 23° 15^; or 



TRANSITS OF THE SEVEJSTEENTH CENTURY. 25 

three minutes of time to the east of Liverpool^ from 
which it is distant twenty -four miles. 

' I wrote also of the expected transit to my younger 
brother, who then resided at Liverpool, hoping that 
he would exert himself on the occasion. This indeed 
he did, but it was in vain : for on the 24th the sky 
was overcast, and he was unable to see anything, 
although he watched very carefully. He examined 
the sun again on the following day, which was some- 
what clearer, but with no better success, Venus having 
already completed her transit. 

^ I hope to be excused for not informing other of 
my friends of the expected phenomenon ; but most of 
them care little for trifles of this kind, preferring rather 
their hawks and hounds, to say no w^orse ; and although 
England is not without votaries of astronomy, Avith 
some of whom I am acquainted, I was unable to con- 
vey to them the agreeable tidings, having myself had 
so little notice. If others, without being warned by 
me, have witnessed the transit, I shall not envy their 
good fortune but rather rejoice, and congratulate them 
on their diligence. Nor will I withhold my praise from 
anyone who may hereafter confirm my observations 
by their own, or correct them by anything more exact. 

' Venus was visible in the sun throughout nearly 
the whole of Italy. France, and Spain ; but in none 
of those countries during the entire continuance of the 
transit. 

' But America ! 

fortiinatos nimium, bona si sua norint. 



26 TRANSITS OF VENUS. 

Venus ! what riches dost thou squander on unworthy 
regions which attempt to repay such favours with gold, 
the paltry product of their mines. Let these bar- 
barians keep their precious metals to themselves, the 
incentives to evil which we are content to do without. 
These rude people would indeed ask from us too much 
should they deprive us of all those celestial riches, the 
use of which they are not able to comprehend. But 
let us cease this complaint, Venus ! and attend to 
thee ere thou dost depart.' 

On which Horrocks bursts into strains of poetry, 
imploring Venus not to seek those barbarous regions 
for which, even as his eyes were gazing upon her, she 
was hastening. ^ But ah ! ' he sighs, ' thou fliest. 

And torn from civil life, 
Tlie savage grasp of wild untutored man 
Holds thee imprisoned in its rude embrace. 
Thou fliest, and we shall never see thee more ; 
"While heaven, unpi tying, scarcely would permit 
The rich enjojmient of thy parting smile. 
Oh ! then farewell, thou beauteous queen ! thy sway 
May soften natures yet untamed, whose breasts, 
Bereft of natiA^e fury, then shall learn 
The milder virtues. We, with anxious mind, 
Follow thy latest footsteps here, and far 
As thought can carry us ; my labours now 
Bedeck the monument for future times 
"Which thou at parting left us. Thy retiu^n 
Posterity shall witness ; years must roll 
Away, but then at length the splendid sight 
Again shall greet our distant children's eyes.' ^ 



THE TRANSIT Oi^ 1761, 2/ 



CHAPTER 11. 

THE TRANSIT OF llQl. 

From the way in which Horrocks showed how the 
apparent place of Venus on the snn's face must be 
affected by the observer's position, it is tolerably clear 
that he would have been led to perceive how obser- 
vations made from different places could be used to 
determine the sun's distance, had time permitted him 
to correspond with other astronomers. For at the 
beginning of Chapter YI. he says : ^ I beheld Venus 
during the transit, not from the centre, but from the 
surface of the earth, therefore I observed her apparent 
and not her true situation. Her true situation, which 
chiefly^ concerns us, is only to be obtained by the 
correction of the parallaxes, into which subject I now 
proceed to inquire. The hypotheses of all astronomers 
make the parallax of Venus in so near an approach to 
the earth sufficiently apparent ; but this I shall leave 
to be further considered in a separate treatise.' He 
then shows how the sun's distance enters into the 
determination of the true from the apparent position. 
At the end of the work he speaks again of the pro- 
posed treatise. ' T had intended,' he says, ' to offer 
a more extended treatise on the sun's parallax; but as 



28 TRANSITS OF VEyUS. 

the subject appears foreign to our present purpose, 
and cannot be dismissed with a few incomj)lete argu- 
ments, I prefer discussing it in a sei)arate treatise — 
" De sijderum dimensione " — which I have in hand. 
In this Avork I examine the opinions and views of 
others ; I fully explain the diagram of Hipj)archus, 
by which the sun's parallax is usually demonstrated, 
and I subjoin sundry new speculations. I also show 
that the hypotheses of no astronomer (Ptolemy not 
excepted — nor even Lansberg, who boasts so loudly 
of his knowledge of this subject) answer to that 
diagram, but that Kepler alone properly understood it. 
I show, in fact, that the hypotheses of all astronomers 
make the sun's parallax either absolutely nothing or 
so small that it is quite imperceptible, whereas they 
themselves, not understanding what they are about, 
come to an entirely opposite conclusion, a paradox of 
which Lansberg affords an apt illustration. Lastly, 
I show the insufficiency and uselessness of the common 
mode of demonstration from eclipses. I give many 
other certain and easy methods of proving the distance 
and magnitude of the sun, and I do the same with 
regard to the moon and the rest of the planets, adducing 
several new observations.' 

There cannot be a doubt, I think, that had Hor- 
rocks lived to complete this treatise, the methods 
subsequently devised by Halley and Delisle would 
have been found included among the ' certain and 
easy methods of proving the sun's distance and mag- 
nitude.' They are so obvious, when once the connec- 



THE TRAXSIT OF 1761. 2g 

tion between transits and the solar parallax has been 
noticed, that they could not possibly have escaped the 
keen insight of the young astronomer^ especially as he 
had actually observed Venus in transit. 

Passing, however, from what might have happened, 
let us consider how, during the interval between 
Horrocks's transit and the next, the idea of utilising 
transits for the determination of the sun's distance 
presented itself to astronomers. 

Priority in this matter has been claimed for James 
Gregory ; but, as Sir Edmund Beckett points out in 
tlie last edition of his ' Astronomy without Mathe- 
matics,' on insufficient grounds. In a scholium to the 
87th problem of his Opiica Proinota^ Gregory says 
that ' the problem has a very beautiful application, 
although pei'haps laborious, in observations of Venus 
or Mercury Avhen they obscure a small portion of the 
sun ; for by means of such observations the parallax 
of the snn may be investigated.' But the method 
described in the problem, the object of which is to 
determine the parallaxes of two planets by observations 
of their conjunctions, has no practical value. I can- 
not understand on what grounds Prof. Grant, in his 
' Physical Astronomy,' claims for Gregory the credit 
usually attributed to Halley. For if the mere mention 
of the connection between the phenomena of a transit 
and the solar parallax be the point, insisted uffon, 
Horrocks seems clearly to have anticipated Gregory ; 
if the method described by Gregory be insisted upon, 
then, since that method never has been and never 



30 TRANSITS OF VENUS. 

could be applied successfully, Gregory cannot be 
regarded as having anticipated Halley, the inventor 
of a practicable method. The very fact that Mercury 
is associated with Venus, in the sentence quoted from 
Gregory's work, shows how little he had grasped the 
idea of Halley's problem, in the solution of which 
transits of Mercury are useless. It is not because of 
the intrinsic importance of the invention that I discuss 
the rival claims ; for I think that the approach of the 
transits of 1761 and 1769 would probably have forced 
the attention of astronomers to the very simple con- 
siderations on which the matter depends. But, as 
Halley had in all probability read the Optica Promota 
(Admiral Smyth thinks Halley had certainly done so^), 
the much more important question whether Halley 
treated Gregory with fairness is really involved. As 
Gregory died in 1675, only four years before Halley 
mentioned the utility of observations of Venus in 
transit, it would seriously affect our estimate of Halley 's 
character if we adopted Prof. Grant's conclusion. I 
think, however, there can be very little question, when 
Gregory's remarks have been carefully studied, that 
Halley must be acquitted of all unfairness. 

On November 7, 1677, Halley, stationed at St. 
Helena, witnessed a transit of Mercury. He noticed 
that the duration of the transit could be observed very 
exactly, and was thus led to believe that the apparent . 

J 

* Nevertlieless, tliis may be doubted, as Halley was but twenty-one 
years old when the idea of utilising transits first occurred to him ; and 
it was only two years later that he announced the idea. 



THE TRAXSIT OF 1761. 3 1 

position of the path of transit of Mercury or Venus 
could be very accurately determined. In 1679, in the 
Catalogus Stellarum. Australium, ^ve find his first 
public mention of the idea. Later, he gave it closer 
attention, and at last, in 1716 (three years before he 
became Astronomer Royal), he contributed to the 
Proceedings of the Royal Society the following paper '^ 
(I quote Ferguson's translation) : — 

^ There are many things exceedingly paradoxical, 
and that seem quite incredible to the illiterate, which 
yet, by means of mathematical principles, may be 
easily solved. Scarce any problem will appear more 
hard or difficult than that of determining the distance 
of the sun from the earth, very near the truth ; but 
even this, when we are made acquainted with some 
exact observations, taken at places fixed upon and 
chosen beforehand, will, ^Adthout much labour, be 
effected. And this is what I am now desirous to lay 
before this illustrious Society (which I foretell will 
continue for ages), that I may explain beforehand to 
young astronomers, who may perhaps live to observe 
these things, a method by w^hich the immense distance 

^ 'It must be admitted,' says Grant of this essay, 'that the ability 
^vith which Halley expounded the peculiar advantages attending the 
determination of the solar parallax by observations of the transits of 
Venus, the earnestness "with -which he recommended the practical ap" 
plication of the method, and the weight of his authority on questions 
relating to astronomical science, were mainly instrumental in inducing 
the different Governments of Europe to adopt those liberal proceedings 
for observing the transits of 1761 and 1769 which hare led to a more 
accurate knowledge of the dimensions of the solar system than could 
otherwise be hoped for.' 



Z2 TRANSITS OF VENUS. 

of the sun may be truly obtained to wirhin a five- 
lundredth part of what it really is. 

' It is well known that the distance of the sun 
from the earth is by different astronomers supposed 
different ; according to what was judged most probable 
from tlie best conjecture that each could form. 
Ptolemy and his followers^ as also Copernicus and 
Tycho Brahe, thought it to be 1,200 semidiameters 
of the earth; Kepler^ 3,500^ nearly ; Ricciolus doubles 
the distance mentioned by Kepler^ and Hevelius onlv 
increases it by one-half. But the planets Venus and 
Mercury, having, by the assistance of the telescope, 
been seen in the disc of the sun, deprived of their 
borrowed brightness, it is at length found that the 
apparent diameters of the planets are much less than 
.hey were formerly supposed; and that the semi- 
diameter of Venus, seen from the sun, subtends no 
more than a fourth part of a minute, or fifteen seconds, 
while the semidiameter of Mercury, at its mean dis- 
tance from the sun, is seen under an angle only of ten 
seconds ; that the semidiameter of Saturn, seen from 
the sun, appears under the same angle ; and that the 
semidiameter of Jupiter, the largest of all the planets, 
subtends an angle of no more than a third part of a 
minute in the sun. Whence, trying the proportions, 
some modern astronomers have thought that the semi- 
diameter of the earth, seen from the sun, would sub- 
tend a mean angle between that larger one subtended 
by Jupiter and that smaller one subtended by Saturn 
and Mercury ; and equal to that subtended by Venus 



THE^ TEAXSIT OF 1761. 33 

— namely^ fifteen seconds — and have thence concluded 
that the sun is distant from the earth almost 1^400 of 
the earth's semidiameters. But the same authors have^ 
on another account, somewhat increased this distance ; 
for inasmuch as the moon's diameter is a little more 
than a fourth part of the diameter of the earthy if the 
sun's parallax should be supposed fifteen seconds, it 
would follow that the body of the moon is larger than 
that of Mercury; that is^ that a secondary planet 
would be greater than a primary^ w^iich would seem 
inconsistent with the uniformity of the mundane 
system. And, on the contrary , the same regularity 
and uniformity seems scarcely to admit that Venus, 
an inferior planet, that has no satellite, should be 
greater than our earth, which stands higher in the 
system, and has such a splendid attendant. There- 
fore, to observe a mean, let us suppose the semi- 
diameter of the earth seen from the sun, or, which is 
the same thing, the sun's horizontal parallax, to be 
twelve seconds and a half — according to which the 
moon will be less than Mercury, and the earth larger 
than Venus — and the sun's distance from the earth 
wall come out nearly 16,500 of the earth's semi- 
diameters. This distance I assent to at present as the 
true one, till it shall become certain what it is by the 
experiment which I propose. Xor am I induced to 
alter my opinion by the authority of those (however 
weighty it may be) who are for placing the sun at an 
immense distance beyond the bounds here assigned, 
relying on observations made upon the vibrations of a 

D 



34 TBA^SITS OF VEXVS. 

pendulum, in order to determine those exceeding small 
angles ; but which, as it seems, are not sufficient to be 
depended upon ; at least, by this method of investigating 
the parallax, it will come out sometimes nothing, or 
even negative — that is, the distance would either 
become infinite, or greater than infinite, which is 
absurd. And indeed, to confess the truth, it is hardly 
possible for a man to distinguish, with any degree of 
certainty, seconds, or even ten seconds, with instru- 
ments, let them be ever so skilfully made. Therefore 
it is not at all to be wondered at that the excessive 
nicety of this matter has eluded the many and in- 
genious endeavours of such skilful operators. 

• About forty years ago, Avhen I was in the island 
of St. Helena, observing the stars about the south pole, 
I had an opportunity of observing, with the greatest 
diligence. Mercury passing over the disc of the sun : 
and (which succeeded better than I could have hoped 
for) I observed, with the greatest degree of accuracy, 
by means of a telescope twenty-four feet long, the 
very moment when Mercury, entering upon the sun, 
seemed to touch its limb within, and also the moment 
when oroino: off it struck the limb of the sun^s disc, 
formino; the ano4e of interior contact : whence I found 
the interval of time, during which Mercury then ap- 
peared within the sun's disc, even without an error of 
one second of time. For the lucid line intercepted 
between the dark limb of the planet and the bright 
limb of the sun, although exceedingly fine, is seen by 
the eye, and the little dent made on the sun's limb. 



i 



THE TRANSIT OF 1761. 35 

by Mercury's entering the disc^ a])pears to yanisli in a 
moment ; and also that made by Mercury leaving the 
disc seems to begin in an instant. When I perceived 
this it immediately came into my mind that the sun's 
parallax might be accurately determined by such kinds 
of observations as these, provided Mercury were but 
nearer to the earth, and had a greater parallax from the 
sun ; but the difference of these parallaxes is so little 
as always to be less than the solar parallax which we 
seek, and therefore Mercury, though frequently to be 
seen on the sun, is not to be looked upon as fit for our 
purpose. 

' There remains, then, the transit of Venus over 
the sun's disc ; whose parallax, being almost as great 
as the solar parallax, will cause very sensible differ- 
ences between the times in which Venus will seem 
to be passing over the sun at different parts of the 
earth. And from these differences, if they be ob- 
served as they ought, the sun's parallax may be 
determined even to a small part of a second. Xor do 
we require any other instruments for this purpose 
than common telescopes and clocks, only good of their 
kind : and in the observers nothing more is needful 
than fidelity, diligence, and a moderate skill in as- 
tronomy. For there is no need that the latitude 
of the place should be scrupulously observed, nor 
that the hom'S themselves should be accurately deter- 
mined with respect to the meridian; it is sufficient 
that the clocks be regulated according to the motion 
of the heavens, if the times be well reckoned from 

D 2 



36 TRANSITS OF VENUS. 

the total ingress of Venus into the sun's disc to the 
beginning of her egress from it ; that is^ when the dark 
globe of Venus first begins to touch the bright limb 
of the sun within ; which moments I know^ by my 
own experience^ may be observed within a second of 
time. 

^ But, on account of the very strict laws by which 
the motions of the planets are regulated, Venus is 
seldom seen within the sun's disc ; and during the 
course of 120 years it could not be seen once — namely, 
from the year 1639 (when this most pleasing sight 
happened to that excellent youth Horrocks, our 
countryman, and to him only since the Creation) to 
the year 1761, in which year, according to the theories 
which we have hitherto found agreeable to the celestial 
motions, Venus will again pass over the sun on May 
26,^ in the morning ; so that at London about five 
o'clock in the morning we may expect to see it near 
the middle of the sun's disc, and not above four minutes 
of a decree south of the sun's centre.^ But the dura- 



* June 6, according to nev style. 

^ The true time of mid-transit was almost tvventj-tliree minntes past 
five, and Yenns, instead of being only 4' sonth of the sun's centre at 
mid-transit, passed more than 9^' below that point. The difference in 
the latter respect was much the more important. Halley was not un- 
aware of the possibility of error in his computation, since the error 
arose from his neglecting the shifting of the nodes of Venus, described 
farther on (p. 108) ; and he notes that possibly the nodes may shift. 

Any exact discussion of the phenomena which the transit would haye 
presented if Halley's computations had been correct would, of course. 
be idle ; but it may l)e as well roughly to indicate the actual difference 
between the transit as it occurred and as Halley computed it. 

In fig. 3, c is the centre of the sun's disc, i e ; i e is the path of 



THE TRAXSIT OF 1761. 37 

tion of this transit will be almost eight hours — namely, 
from two o'clock in the morning till almost ten. Hence 

Venus, as computed by Halley ; i e is the path, she actually traTersecl. 
The time occupied in traversing i e was about 6J horn's, whereas the 




Fig. 3. — IlliLStrating the Transit of Venus in 1761, as it actually 
occurred, and as Halley computed it. 

time which would have been occupied in traversing i e amounts to close 
upon eight hours, being very little less than that occupied in a central 
transit. It is manifest, at once, that the chords of transit i e are much 
more nearly equal than the chords, i e, so that as far as mere length of 
transit chord is concerned it would be useless to set the observers far 
apart in a northern and southern direction. But what Halley hoped to 
do was this : — 

Let p, fig. 4, be the Xorth pole of the earth, travelling in the direction 
indicated by the arrow, p being in sunlight, as the date is June 6. The 
equator is represented by e' e e. Xow, suppose for a moment that an 
observer at e sees Venus in the direction e v (Venus herself being sup- 
posed to lie far beyond the picture on the right, and above the level of 
the paper, to correspond to the shape given to the terminator between 
light and darkness on the earth). Then, at this moment an observer 
at A sees Venus in direction a v, or apparently not so far advanced (since 
she comes between the earth and sun, moving in the same direction as 
the earth around the sun, and with a greater velocity). On the other 
hand, the observer at a' sees her in direction a' i/, or apparently farther 



38 TRANSITS OF VENUS. 

the ingress will not be visible in England ; but as the 
sun will at that time be in the sixteenth deoree of 



advanced. Hence tlie effect of being carried from a to a' is to throw 
Venns forward on lier path. But an observer at a, when transit began, 



±ig. 4.— lllnstratiug the Conditions of the Transit of 1761, 
as computed by Halley. 

would be carried by the earth's rotation, diunng the transit (lasting 
nearly eight hours) to the position a' ; to him, therefore, the dura- 
tion of the transit would be shortened by the earth's rotation. But 
next consider three observers in the latitude parallel a b a, near to the 
pole. The observer at h sees Venus in direction b v; from a she is seen 
towards w, or thrown forwards; from a' she is seen towards w', or 
thrown backwards. The effect of being carried from a to a is, then, to 
throw Venus back, or lengthen the duration of her transit. Now, if we 
set an observer so that at the beginning of the transit he is at a, he will 
be carried to the position a at the end of the transit, if only we so select 
the latitude parallel a a' that the part in the darkened hemisphere cor- 
responds to rather less than eight hours' rotation ; in other words, take a 
latitude where, on June 6, or 15 days before midsummer, the night lasts 
less than eight hours. We find latitude bQ>° North suitable. This would 
give the beginning of the transit at sunset and the end at sunrise ; and 
the whole of the transic between the contacts invisible. But as the sun 
must not be exactly on the horizon at the critical moments, we must 
.<ike a place in somewhat higher latitude than 56° ; and of course, the 



THE TRANSIT OF 1761. 39 

Gemini/ having almost twenty-three degrees north 
declination^ it will be seen without setting at all, 

longitude of a, as of a, would depend on the time at whicli transit 
began, since we must have the station which is at a at the beginning 
carried to the position e, at the middle. According to Halley's computa- 
tion the middle of the transit would occur at about 5 in the evening, or 
E must be in seven hours east longitude at mid-transit. This, then, is the 
longitude of the equatorial station ; and the longitude of the northern 
station is therefore to be in five hours west longitude. 

Plate IV. would have to be thus altered to illustrate the circum- 
stances of the transit as computed by Halley : — The two projections, 
instead of touching in Sumatra, should touch about a third of an hour 
farther east ; since c a corresponds to the length of transit, the points 
A and D should be brought nearly two hours in longitude nearer together ; 
and of course a' and d' should be shifted to correspond. The point 
I would move to a place near the new position of a', i' to a point near 
the new position of b, e near to the new position of d, and e' near the 
new position of d. Thus, h, which is the middle of the arc e i, would 
come close to Sumatra, and h' would be near the G-alapagos Islands. 
It would haA^e been easy to find a number of stations near h in its new 
position ; but the region e m i, much increased by the shifting of A b 




Fig. 5. — Illustrating the changes to be made in Plate IV., in order that 
it may correspond to the transit of 1761, as computed by Halley. 

and c D, would be the best part, so far as approach to the new position 
of h' was concerned. It will be seen that, under -the actual conditions 
of the transit, the region m e was quita imsuited for the purpose which 



40 TRANSITS OF VENUS. 

in almost all parts of the north frigid zone ; and there- 
fore the inhabitants of the north coast of Norway, 
beyond the city of Nidrosia, which is called Drontheim, 
as far as the North Cape, will be able to observe Venus 
entering the sun's disc ; and perhaps the ingress of 
Venus upon the sun when rising will be seen by the 
Scotch, in the northern parts of the kingdom, and by 
the inhabitants of the Shetland Isles, commonly called 
Thule. But at the time when Venus will be nearest 
the sun's centre the sun will be vertical to the northern 
shores of the Bay of Bengal, or rather over the kingdom 
of Pegu ; and therefore in the adjacent regions, as the 
sun, when Venus enters his disc, will be almost four 
hours towards the east, and as many towards the west 
at the time of her egress, the apparent motion of Venus 
on the sun will be accelerated by almost double the 
horizontal parallax of Venus from the sun ; because 
Venus at that time is carried with a retrograde motion 
from east to west, while an eye placed upon the earth's 
surface is whirled the contrary way, from east to west. 
Supposing the sun's parallax (as we have said) to be 
12^^^, the parallax of Venus will be 43^^ ; from which, 
subtracting the parallax of the sun, there will remain 
30^^ at least for the horizontal parallax of Venus from 
the sun ; and therefore the motion of Venus will be 
increased 45^^ at least by that parallax, w^hile she passes 
over the sun's disc in those elevations of the pole 

had led Halley to indicate it for occupation ; and the nearest approach 
to h' was within the space d' on' a\ near m'. Fig. 5 illustrates the con- 
ditions of transit as computed by Halley. 



THE TRANSIT OF 17QI. 4 1 

which are In places near the tropic, and yet more in 
the neighbourhood of the equator. Now, Venus at 
that time will move on the sun's disc very nearly at 
the rate of four minutes of a degree in an hour ; and 
therefore eleven minutes of time at least are to be 
allowed for 45^^, or three-fourths of a minute of a 
degree ; and by this space of time the duration of this 
eclipse caused by Venus will, on account of the parallax, 
be shortened. And from this shortening of the time 
only we might safely enough draw a conclusion con- 
cerning the parallax which we are in search of, pro- 
vided the diameter of the sun and the latitude of 
Venus were accurately known. But we cannot expect 
an exact computation in a matter of such subtility. 

' We must endeavour, therefore, to obtain if possible 
another observation, to be taken in those places where 
Venus will be in the middle of the sun's disc at mid- 
night ; that is, in places under the opposite meridian 
to the former, or about six hours or ninety degrees 
west of London, and where Venus enters upon the 
sun a little before its setting, and goes off a little after 
its rising. And this will happen under the above- 
mentioned meridian, and where the elevation of the 
north pole is about fifty -six degrees ; that is, in a part 
of Hudson's Bay near a place called Port Nelson. 
For, in this and the adjacent places, the parallax of 
Venus will increase the duration of the transit by at 
least six minutes of time ; because while the sun from 
its setting and rising seems to pass under the pole, 
those places on the earth's disc will be carried with a 



42 TRAKSITS OF VEXVS. 

motion from east to west contrary to the motion of the 
Ganges ; that is, with a motion conspiring with the 
motion of Venus; and therefore Venus will seem to 
move more slowly on the sun, and to be longer in 
passing over its disc. 

^ If therefore it should happen that this transit should 
be properly observed by skilful persons at both these 
places, it is clear that its duration Avill be seventeen 
minutes longer as seen from Port Xelson, than as 
seen from the East Indies. Nor is it of much con- 
sequence (if the English shall at that time give any 
attention to this affair) whether the observation be 
made at Fort George, commonly called Madras, or 
at Bencoolen, on the western shore of the island of 
Sumatra, near the equator. But if the French should 
be disposed to take any pains herein, an observer may 
station himself conveniently enough at Pondicherry, 
on the west shore of the Bay of Bengal, where the 
altitude of the pole is about twelve degrees. As to 
the Dutch, their celebrated mart at Batavia will afford 
them a place of observation fit enough for the purpose, 
provided they also have but a disposition to assist in 
advancing, in this particular, the knowledge of the 
heavens. And indeed I could wish that many obser- 
vations of this famed phenomenon might be taken by 
different persons at separate places, both that we 
mio^ht arrive at a o-reater deo;ree of certaintv bv their 
agreement, and also lest any single observer should 
be deprived by the intervention of clouds of a sight 
w^iich I know not whether anv man livino; in this or 



THE TRANSIT OF 1761. 43 

the next age will ever see again ; and on which depends 
the certain and adequate solution of a problem the 
most noble^ and at any other time not to be attained 
to. I recommend it therefore again and again to those 
curious astronomers who (when I am dead) will have 
an opportunity of observing these things, that they 
would remember this my admonition, and diligently 
apply themselves with all their might in making this 
observation, and I earnestly wdsh them all imaginable 
success : in the first place, that they may not by the 
unseasonable obscurity of a cloudy sky be deprived of 
this most desirable sight, and then, that having ascer- 
tained with more exactness the magnitudes of the 
planetary orbits, it may redound to their immortal 
fame and glory. 

' We have now" shown that by this method the 
sun's parallax may be investigated to within its 500th 
part, w^hich doubtless wdll appear w^onderful to some. 
But if an accurate observation be made in each of 
the places above marked out, we have already demon- 
strated that the durations of this eclipse made by 
Venus will differ from each other by 17 m. of time; 
that is, upon a supposition that the sun's parallax is 
J 2^'\ But if the difference shall be found by obser- 
vation to be greater or less, the sun's parallax will be 
greater or less nearly in the same proportion. And 
since 17 m. of time are answerable to 12^^^ of solar 
parallax, for every second of parallax there will arise 
a difference of more than 80 s. of time ; w^hence if we 
have this difference true to two seconds it will be certain 



44 TRANSITS OF VENUS, 

what the sun's parallax is to within a 40th part of V ; 
therefore his distance will be determined to within its 
500th part at least, if the parallax be not found less than 
what we have supposed : for 40 times \2\ make 500. 

' And noAv I think that I have explained this 
matter fully, and even more than I needed to have 
done to those who understand astronomy ; and I would 
have them take notice that on this occasion I have 
had no regard to the latitude of Venus, both to avoid 
the inconvenience of a more intricate calculation, 
w^hich would render the conclusion less evident, and 
also because the motion of the nodes of Venus is not 
yet discovered, nor can be determined but by such 
conjunctions of the planet with the sun as this is. 
For w^e conclude that Venus will pass four minutes 
below the sun's centre, only in consequence of the 
supposition that the plane of Venus's orbit is im- 
movable in the sphere of the fixed stars, and that its 
nodes remain in the same places where they were 
found in the year 1639. But if Venus in the year 
1761 should move over the sun in a path more to the 
south, it will be manifest that her nodes have moved 
backwards among the fixed stars ; and if more to the 
north, that they have moved forwards; and that at 
the rate of 5^^ of a degree in 100 Julian years, for 
every minute that Venus's path shall be more or less 
distant than the above-said 4/ of the sun's centre. 
And the difference between the duration of these 
eclipses will be somewhat less than 17 m. of time, on 
account of Venus's south latitude ; but greater if by 



TRE TRANSIT OF 1761. 45 

the motion of the nodes forwards she should pass on 
the north of the sun's centre.' 

The rest of Halley's dissertation I omit, because 
it relates to the details of the transit as incorrectly- 
computed by him, and therefore possesses no present 
interest. 

As I have said it was not until three years after 
his essay appeared that Halley became Astronomer 
Royal. It does not appear that during the remaining 
years of his life he made any farther contribution to 
the subject. He died on January 14, 1742, more 
than nineteen years before the transit occurred. 

As the time for the transit drew near astronomers 
began to examine carefully the motions of Venus, in 
order to ascertain how far the conditions on w^hich 
Halley's computation had been based were really 
fulfilled. Passing over, however, a paper by Tre- 
buchet, pointing out inaccuracies in Halley's disser- 
tation, it was not until August 1760, or less than a 
year before the transit took place, that the conditions 
on which successful observation depended were pointed 
out by Delisle. He published a chart of the earth 
on an equatorial projection, showing the hour at which 
the transit would begin or end. The chart corresponded, 
, in fact, to Plate IV., meridional projections being sub- 
I stituted for the equatorial projections there used. It 
^vill be understood, however, that Delisle did not claim 
for his chart the degree of accuracy aimed at in 
I Plate IV. He showed that the stations selected by 
Halley were not suited to the actual conditions of the 



46 TRAXSITS OF VEXUS. 

transit, and that in fact the transit could not be well 
observed by the method of durations. He showed 
how, at suitably selected stations, whose longitude had 
been accurately determined, the single observation of 
a contact, w^h ether at ingress or egress, would supply 
the means of determining the solar parallax. For 
the description of his method the reader is referred to 
Chapter IV. 

Ferguson, in England, seems to have independently 
arrived at the same conclusion, not long after; at least 
his treatise on the subject suggests the impression that 
he had selected his own method of dealing with it, and 
had carried his analysis nearly to its completion when 
Delisle's paper and map reached him. He found that 
' instead of passing only four minutes of a degree below 
the sun's centre, Venus will pass almost ten minutes of 
a degree below it, on w^hich account the line of the 
transit will be so much shortened as will make her 
passage over the sun's disc about an hour and twenty 
minutes less than if she passed only four minutes below 
the sun's centre at the middle of her transit ; and 
therefore her parallax from the sun will be so much 
diminished, both at the beginning and end of her transit^ 
and at all places from w^hich the whole of it will be 
seen, that the difference of its duration, as seen from 
them, and as supposed to be seen from the earth's 
centre, will not amount to eleven minutes of time. But 
this is not all; for although the transit will begin 
before the sun sets to Port Nelson, it will be quite * 
over before he rises to that place next morning, on 




; ti^ ' 



'; n^' 



THE TRAySIT OF 1761. 47 

account of its ending so much sooner than as given by 
the tables to which Dr. Halley was obliged to trust. 
So that we are quite deprived of the advantage that 
otherwise would have arisen from observations made at 
Port Xelson.' 

Ferguson gave a chart of the transit on the same 
plan as I have used in Plates II.-IX. The chart 
was taken directly from Delisle, however^ as Fergu- 
son tells US5 only ' I have changed/ he says^ ' his 
meridional projections into that of the equatorial; by 
which I apprehend that the curved lines showing at 
what places the transit begins or ends with the rising 
or setting sun appear more natural to the eye and 
are more fully seen at once than in the map from 
which I copied ; for in that map the lines are inter- 
rupted and broken in the meridian that divides the hemi- 
sphere, and the places where they should join cannot be 
perceived so readily by those who are not well skilled 
in the nature of the stereographical projections.' It 
shows how clear an insio^ht Fero;uson had obtained into 
the conditions of the transit, that, commenting on his 
charts, in which the line, B A of Plate IV., passes down 
the eastern shore of the Red Sea, while a! b' crosses 
Madagascar, he says : ' I question much whether the 
transit will begin at sunrise to any place in Africa that 
is west of the Red Sea, and am pretty certain that the 
sun will not be risen to the northernmost part of Mada- 
gascar when the transit begins, so that the line,' corre- 
sponding to A B, A^ B^ of Plate IV., ' seems to be a little 
too far west in the map at all places which are south 



48 TRANSITS OF VENUS. 

of Asia Minor; but in Europe I think it is very 
well.' 

The actual circumstances of the transit of 1761 in 
different parts of the earth can be inferred with suffi- 
cient accuracy from what is shown in Plate IV. Here 
the arcs A i b and A^ i^ B^ separate the dark and light 
hemispheres of the earth at the beginning of the transit, 
while the arcs c E d and c' e' d^ separate the dark and 
light hemispheres at the end of the transit. Thus the 
beginning of transit was visible at all places on the 
hemisphere formed by combining the sections A i bd and 
A^ i^ B^ D^/and the end of the transit was visible at all 
places on the hemisphere formed by combining the 
sections c e d a and c' e' d' a^ The whole of the 
transit was visible over the spaces T> e i x and d^ mf a^ ; 
but in the space i m e, though the beginning and end 
of the transit were seen^ the progress of the transit 
was not wholly visible. No part of the transit Avas 
visible over the spaces b ^ c and b^ f / c^ ; but in 
the space i^ m' e\ though neither the beginning nor 
the end were visible, the progress of the transit was 
partially visible. At all points of the arcs A i b and 
A^ i^ B^ the ingress occurred with the sun on the horizon ; 
but whereas the sun was rising for the arcs A ^ and ^ i ^ 
he was setting for the arcs B i and b^ i : at all points 
of the arcs c e D and c^ E^ d' the egress occurred with 
the sun on the horizon ; but whereas the sun was 
rising for the arcs c e and c^ e\ he was setting for the 
arcs D e and D^ e\ At the points m and m^ the sun 
was on the horizon both at ingress and at egress ; but 



THE TRAXSIT OF 1761. 49 

whereas the progress of the whole transit, except ingress 
and egress, took place during the night at m^ it took 
place during the day at m , In all that has here been 
said, the passage of Venus's centre has been alone con- 
sidered. 

The point i^ was that where ingress occurred 
earliest, the point i being that where ingress occurred 
latest. It was around these points, then, that observers 
of ingress by Delisle's method were to be placed, keep- 
ing, of course, to that side of the arcs a! b' and A B 
on which the sun would be above the horizon at the 
time of ingress. We see that several islands were con- 
veniently placed near 1' for showing accelerated ingress, 
though they were not very well known in those days. 
The eastern parts of Arabia and parts of India 
afforded convenient stations near i for observing re- 
tarded ingress. 

The point E was that where egress occurred earliest, 
e' being that where egress occurred latest. Kams- 
chatka, Japan, and Manchooria afforded convenient 
stations for observing accelerated egress, while the Cape 
of Good Hope was well placed for observing retarded 
egress.^ 

As regarded the application of Halley's method — 
that is, the observation of duration where greatest and 
least — the transit was not a favourable one. H was the 



^ Encke. in ] 822. found the follo^ng elements for tlie transit of 
1761. I quote them from the excellent little treatise, 'Les Passages de 
Tenus sur le disqne Solaire,' by M. Dubois. Xaval Examiner in Hydro- 

graphyfor France, substituting G-reen^nchfor Paris time and longitude. 

E 



50 



TRANSITS OF VENUS, 



place where transit had the shortest duration, H^ being 
the place where, if the transit had been visible, its 
duration would have been least. Stations near h 
could of course be occupied, as here the summer of 
Siberia was in progress. But we see that there was 
no station at all near to H^ Avhence the whole transit 
could be seen. The point m^ was geometrically the 
most advantageous, but there the sun was upon the 
horizon. The south-western extremity of Austraha or 
the island of St. Paul were the only regions available, 
and they were almost as far from H^ as from H. In 
point of fact, Halley's method failed totally on this 
occasion. It commonly fails at the earlier transit of a 
pair separated by eight years, as will be shown in the 
next chapter; but it is worthy of notice that the 
circumstances of the transit of 1761 in this respect 
Avere very nluch like those of the coming transit of 
1882. Althouo-h the transit of 1882 will be the 



and correcting a misprint, by which in one place north and south lati- 
tudes are interchanged :- 





h. 


m. 


s. 






Ingress of Venus's centre 


. U 


12 


48-5 


] Gr 
f ap 
J sol 


senwich 


Middle of the transit 


. 17 


23 


0-0 


parent 


Egress of the centre 


. 20 


29 


13-5 


ar time. 


Duration of the transit . 


. 6 


16 


25-0 






Least distance of centres . 


. 


9 


34-2 






' 


Latitude 




Longitude 


Pole of accelerated ingress 


o 

. 20 


56 S 




o 

132 


28 W 


„ ,, retarded „ . 


. 20 


56 N 




47 


32 E 


„ „ accelerated egress 


. 46 


47 N 




167 


59 E 


„ ,, retarded ,, 


. 46 


47 S 




12 


\ys 


„ „ shortened durations . 


. 52 


31 N 




92 


42 E 


„ ,, lengthened „ . 


. 52 


31 S 




87 


18 W 



THE TRANSIT OF 1761. 5 1 

second transit of a paii% its geometrical superiority is 
counterbalanced by the inaccessibility of the antarctic 
as compared with the arctic regions. 

I do not know that any useful purpose could be 
served by inserting here an account of the various 
observations of the transit of 1761 made by the persons, 
176 in number, who took a more or less important share 
in the work at no less than 117 stations. Presently 
the peculiar phenomena which rendered the observation 
of internal contact uncertain will be described; but 
the mere records of time observations have no special 
interest. A few examples may suffice to show this. 

We see from Plate IV. that the beo;innino; of the 
transit was invisible in the western parts of Europe, 
but the latter half was visible there, though not under 
specially advantageous circumstances. We have the 
"alloAving particulars respecting the observations in 
London at Greenwich : ' Early in the morning, when 
every astronomer was preparing for observing the 
transit, it unluckily happened that, both at London and 
the Royal Observatory at Greenwich, the sky was so 
overcast with clouds as to render it doubtful whether 
any part of the transit would be seen, and it was 38 m. 
21 s. past 7 o'clock, apparent time, at Greenwich when 
the Rev. Mr. Bliss, our Astronomer Royal, first saw 
Venus on the sun. . . From that time to the beo^innino; 
of egress the Doctor made several obseivations, both of 
the difference of right ascension and declination of the 
centres of the sun and Venus, and at last found the 
beginning of egress, or instant of the internal contact 

E 2 



52 TR AX SITS OF VEXUS 

of Venus with the sun's limb^ to be at 8 hours 1 9 minutes 
seconds apparent time. . . . By the means of three 
good observations the diameter of Venus on the sun 
was 58 seconds of a degree.' ' Mr. Short made his 
observations at Savile House, in London, 30 seconds 
in time west of Greenwich, in presence of His Eoyal 
Highness the Duke of York, accompanied by Their 
Royal Highnesses Prince William, Prince Henry, and 
Prince Frederick.' So the account runs. We are not 
told whether the Duke of York actually honoured 
Venus by directing His Royal gaze upon her during her 
transit, or whether Their Other Royal Highnesses made 
any observations ; but as Venus was under observation 
for about 3|- hours, we may suppose that these exalted 
persons did not lose the opportunity of witnessing a 
phenomenon so seldom seen. Venus, all unconscious of 
the honour, moved onwards to eg-ress, contact occurrino; 
at 8 h. 18 m. 15-J- s. apparent Green^vich time, or 
8^ s. sooner than at Greenwich. At Stockholm the 
whole transit was observed by Wargentin, the whole 
duration (between the internal contacts) being 5 h. 
50 m. 45 s., corresponding to a little over six hours 
for the passage of the centres. At Stockholm, as we 
see from Plate IV., the transit was shortened as com- 
pared with the mean duration. 

Chappe d'Auteroche was stationed at Tobolsk, in 
Siberia — an important station for the Halleyan method 
(see Plate IV.), if any stations had been available 
for observino; lengthened durations. The transit, as 
observed by him, lasted 5 h. 48 m. o2\ s., or nearly 



THE TRANSIT OF 1761. 53 

2 m. less than at Stockholm. Chappe had some 
trouble in reaching Tobolsk in time for his observations. 
He started at the end of November 1760^ and reached 
St. Petersburg readily enough ; but the journey 
thence to Tobolsk was not completed without incon- 
venience and even serious dangers. He reached 
Tobolsk on April 10, 1761, the voyage having lasted 
five months. 

England sent out an expedition intended for Ben- 
coolen, in Sumatra, apparently because that station had 
been mentioned in Halley's dissertation ; for Sumatra, 
almost midway between H and m! (Plate IV.), offered 
no advantages for the observation of durations, and was 
altogether too far removed both from i and E to be of 
the least service as a Delislean station. Fortunately the 
ship was attacked by a Spanish war-ship on the road, 
and had to put in at the Cape, where very useful obser- 
vations of the retarded egress were made. Another 
English expedition was sent to St. Helena, a station 
where retarded egress was observable, but by no 
means advantageously. At Madras, Mr. Hirst, and 
at Calcutta, Mr. Magee (whom M. Dubois converts 
into Magec) observed the duration of transit, obtain- 
ing respectively the periods 5 h. 51 m. 43 s., and 5 h. 
50 m. 36 s., values which differ much more from each 
other than parallax will account for. As Ferguson well 
remarks of the whole series of observations : ' Whoever 
compares the times of the internal contacts, as given 
by different observers, will find such difference among 
them, even those which were taken from the same spot, 



54 TRANSITS OF VENUS. 

as will show that the instant of either contact could 
not be so accurately perceived by the observers as 
Dr. Halley thought it could^ which probably arises 
from the difference of people's eyes and the different 
magnifying powers of those telescopes through which 
the contacts were seen. If all the observers had made 
use of equal magnifying powers there can be no doubt 
that the times would have more nearly coincided^ since 
it is plain that^ supposing all their eyes to be equally 
quick and good^ they v>^hose telescopes magnified most 
could perceive the point of internal contact soonest 
and of the total exit latest.' 

Le Gentil^ who had been appointed to observe at 
Pondicherry^ was very unfortunate. The following 
account is taken from M. Dubois' admirable work 
already referred to : ' On account of the distance of 
the station where he was to observe the transit, Le 
Gentil set out from France on March 26^ 1760. The 
observation he hoped to make at Pondicherry was 
curious and interesting, says J. D. Cassini; in fact, he 
would have seen the whole transit, and the middle 
would have occurred when the sun was nearly on the 
meridian at about ten degrees from the zenith. Le 
Gentil arrived at the Isle of France on July 10, 1760, 
that is to say, nearly a year before the expected 
transit ; but the war which arose at that epoch between 
France and England rendered it no longer possible 
for him to go to Pondicherry. He resolved to betake 
himself to Rodriguez, awaiting meanwhile the pro- 
gress of events. He was just setting off for this new 



THE TRANSIT OF 1761. 55 

station, where also De Pingre was to observe, when he 
learned that a French frigate was about to leave the 
Isle of France for the coast of Coromandel. Le Grentil 
resolved to avail himself of this opportunity to go to 
the place selected by the Academy of Sciences ; but 
he was not able to leave the Isle of France on board 
this frigate till about the middle of March 1761. It 
was already very late. The frigate carrying the 
French astronomer experienced at first long-continued 
calms, which were enough to cause Le GentU to 
despair, and which did not permit him to reach the 
coast of Malabar before May 24. To increase his ill- 
fortune, the commander of the frigate learned that the 
English were masters of Mahe and Pondicherry. Tlie 
frio^ate had no other resource but to take flio;ht without 
delay. This she did ; and, to the utter despair of Le 
Gentil, she retook her way towards the Isle of France. 
The 6th of June arrived! The frigate was in 87"^ 
East longitude (from Paris), and 5° 45^ South latitude. 
The sky was clear, the sun splendid ! The unfortunate 
Le Gentil, unwilling to be altogether idle, observed 
the transit on board the ship, taking all possible care. 
He noted the times of ingress and egress ; but with 
what degree of approximation were those times ob- 
tained, even admitting that those he noted coincided 
exactly with the instant of the contacts ? The voyage 
of the French Academician ended thus in failure. 
Le Gentil then experienced one of those mishaps which 
p,ssume to the man of science all the proportions of a 
real misfortune — to have traversed so large a portion of 



56 TRANSITS OF VENUS. 

the globe, to have endured all the weariness, all the 
privations, all the perils of a long sea- voyage, and to 
effect nothing ! This was enough to have disgusted 
anyone with scientific observation, or at least with 
Halley's method. We shall presently see, however, 
when dealing with the transit of 1769, that Le Gentil, 
so far as that method was concerned, had not yet seen 
the last of his troubles.' 

De PIngre reached Rodriguez In May 1761 ; and 
although he had to observe in the open air, and could 
scarcely find a place where to keep his clock out of the 
wind, his observations were among the best of those 
eflfected during the transit of 1761. 

The results of the observations were far from 
satisfactory, the values of the solar parallax deduced 
by mathematicians ranging between 8^^'5 and 10^^*5, 
corresponding to a distance of the sun ranging from 
96,162,840 miles to 77,846,110 miles. From a com- 
parison of a great number of observations made by 
Short the parallax 8^^ '5 was deduced for the day of 
the transit, corresponding to 8^''*65 for the earth's 
mean parallax, or a distance of 94,498,420 miles. In 
1822, Encke, then sub-director at Seeberg, deduced 
from the observations made in 1761 a parallax lying 
between the extreme limits 8'' -429813 and 8''-ool237, 
corresponding to the distances 97,000,000 miles and 
95,600,000 miles. 

These discrepancies were no doubt due to two 
chief causes. In the first place, the observations were 
mostly Dellslean, and in the last century means did 



THE TRAXSIT OF 1761. 57 

not exist for the determination of the longitude with 
the degree of accuracy which was required. Secondly^ 
it was found that the phenomena attending the ingress 
and egress of Venus are not so simple as Halley had 
supposed^ when he stated that the time of internal con- 
tacts can be determined within a single second of time. 
Halley had reckoned on the appearances presented 
during a transit such as he had observed at St. 
Helena^ when the sun was high above the horizon^ 
and the small disc of Mercury was little disturbed by 
atmospheric effects. But at most of the stations 
for effectively observing the transit of Venus in 1761, 
and at all those best suited for applying Delisle's 
method, the sun was not far from the horizon, and the 
outline of Venus was seriously affected by atmospheric 
undulations. Moreover, an optical phenomenon which 
had not attracted Halley's attention was presented 
during the transit of 1761, and caused the observations 
to be much less reliable than they would otherwise 
have been. The disc of Venus was found to assume 
near the time of internal contact a distorted form. In 
some cases she seemed to be attached to the edge of 

W W K 

Fig. 6. — Illustrating the Black Drop. 

the sun by a dark ligament of greater or less breadth, 
as shown at 1^2, and 3, fig. 6 ; in other cases she 



58 TRANSITS OF VENUS, 

appeared shaped like a pear^ while in others she was 
altogether distorted by the combined effect of atmo- 
spheric disturbances and the optical distortion (wliat- 
ever its real nature may be) wdiich causes the black 
drop and pear-shape figures. 

This was the first occasion on which the peculiar 
appearances in question w^ere noted ; but as the diffi- 
culty thus introduced affected the discussion of the 
observations made during both the transits of the last 
century, this will be a convenient place for describing 
what was seen in 1769 as Avell as in 1761. Professor 
Grant has collected together in his fine ^ History of 
Physical Astronomy ' several of the most interesting 
observations of this kind, and from his work I quote 
the following cases; — 

^Mr. Hirst, who observed the transit of 1761 at 
Madras, stated that ' at the total immersion the planet, 
instead of appearing truly circular, resembled more 
the form of a bergamot pear, or, as Governor Pigott 
then expressed it, looked like a ninepin ; yet the pre- 
ceding limb of Venus w^as extremely well defined.' 
With respect to the end of the transit, he remarked 
' that the planet was as black as ink, and the body 
truly circular, just before the beginning of egress, yet 
it was no sooner in contact with the sun's preceding 
limb, than it assumed the same figure as before at the 
sun's subsequent (following) limb; the subsequent limb 
of Venus keeping well-defined and truly circular.' 

A. similar appearance w-as observed by Salunde at 
Paris, by Bergman at Upsal, and also by several othe^ 
Individuals. 



THE TRANSIT OF 1761. 59 

Dr. Maskelyne^ who observed the transit of 1769 
at Greenwich, gives the following description of a 
phenomenon of a similar nature witnessed by him at 
the egress of the planet : — 

' The regularity of Venus's circular figure was 
disturbed towards the place where the internal contact 
should happen by the addition of a protuberance dark 
like Venus and projecting outwards, which occupied 
a space upon the sun's circumference which bore a con- 
siderable proportion to the diameter of Venus. Fifty- 
two seconds before the thread of light was formed, 
Venus's regular circumference (supposed to be con- 
tinued as it would have been without the protuberance) 
seemed to be in contact with the sun's circumference, 
supposed also completed. Accordingly, from this time 
Venus's regukr circumference (supposed defined in the 
manner just described) appeared wholly within the 
sun's circumference, and it seemed, therefore, wonderful 
that the thread of lio;ht should be so lono; before it 
appeared, the protuberance appearing in its stead. 
At length when a considerable part of the sun's cir- 
cumference (equal to one-third or one-fourth of the 
diameter of Venus) remained still obscured by the 
protuberance, a fine stream of light flowed gently 
round it from each side, and completed the same in 
the space of three seconds of time. But the protube- 
rance, though diminished, was not taken away till about 
twenty seconds more ; when, after being gradually 
reduced, it disappeaied, and Venus's circular figure 
was restored. 



6o TRANSITS OF VENUS. 

Dr. Bevis states in the account of his observations 
that ' the planet seemed quite entered upon her disc, 
her upper limb being tangential to that of the sun ; 
but instead of a thread of light, which he expected 
immediately to appear between them, he perceived 
Yenus to be still conjoined to the sun's limb by a 
slender tail, nothing near so dark as her disc, and 
shaped like the neck of a Florence flask. The said 
tail vanished at once ; and for a few seconds after, the 
limb of Venus, to which it had been joined, appeared 
more prominent than her lower part, somewhat like 
the lesser end of an egg, but soon resumed its rotun- 
dity.' 

The Rev. Mr. Hirst thus describes the appearance 
presented during the transit : ^ The same phenomena 
of a protuberance which I observed at Madras in 1761, 
at both internal contacts, I observed again at this last 
transit. At both times the protuberance of the upper 
edge of Venus diminished nearly to a point before the 
thread of light between the concave edge of the sun 
and the concave edge of the planet was perfected, 
when the protuberance broke off from the upper edge 
of the sun, but Venus did not assume its circular form 
till it had descended into the solar disc some distance.' 

Mr. Dunn, who observed the transit at Greenwich, 
remarks that ' he saw the planet held as it were to the 
sun's limb by a ligament formed of many black cones 
whose bases stood on the limb of Venus, their vertices 
pointing to the limb of the sun.' 

' Mr. Pigott states that Venus, before she separated 



THE TBAXSIT OF 1761. 6 1 

from the sun^ was considerably stretched out towards 
his limb^ which gave the planet nearly the form of a 
pear; and even after the separation of the limbs Yenus 
was twelve or nine seconds before she resumed her 
rotundity.' 

The following cases^ with their accompanying illus- 
trations^ serve at once to indicate the nature and 
suggest the explanation of the peculiar appearances 
presented by Venus when nearly at internal contact. 

Fig. 7 represents the appearance presented by 
Venus as observed by Mayer at St. Petersburg^ in 
1769. A reference to Plate V. will show that at St. 




Fig. 7. — Appearance presented by Venns at Internal Contact, as 
observed by Mayer. 

Petersburg the sun was almost upon the horizon at 
the moment of ingress, and close to the horizon at the 
moment of egress. There can be no doubt that the 
distorted appearance of Venus is due to atmospheric 
disturbances, such as are always recognisable when 
the sun is observed low doAvn. I may remark that 
fig. 7 corresponds precisely to what I observed when 
examinino; the artificial transit of Venus as arrangfed 
at Washington, on a morning when the atmosphere 
was unusually disturbed. The American astronomers 



62 TRANSITS OF VENUS. 

consider that the corresponding arrangements at Green- 
wich are not so good as their own, because the distance 
between the observer and the artificial ' Sun and Venus' 
is not great enough to permit the study of these at- 
mospheric effects. We see clearly enough from Mayer's 
observation that such effects, though they would not 
be nearly so great with the sun even moderately raised 
(say 10°) above the horizon, must always be taken 
into account. The edge of the sun even at a con- 
siderable height is always rippled by the effects of 
atmospheric undulations. So also necessarily must 
the outline of Venus be rippled, and it is the contact 
of two rippling outlines, not of two sharply defined 
discs, that the astronomer is called upon to observe. 

The next picture (fig. 8) is from a drawing by Bay ley 
at Nord C^p. In this case the sun was raised about 



'"li'V'}p'P 



ii 



Fig. 8. — Contact of Venus, as observed by Bayley at Nord Cap. 



10° from the horizon, but the blurred outline given to 
the sun indicates the existence of imperfect atmospheric 
conditions, and we may partly attribute to this cause 
the wideness of the connecting ligament when contact 
was actually established. 

Fig. 9 is from a drawing by Hirst, who observed 
the ingress at Greenwich ; while fig. 10 shows how 



1 



THE TBAXSIT OF 1761. 63 

Venus appeared to Bevis^ who observed at Kew under 
nearly the same conditions. 




Fig. 9.— The BLick Drop, as ol served Lv Hirst. 

There has been much discussion as to the cause 
of the ' black drop/ and in some instances considerable 
energy has been e^^inced in the attempt to show that 




Fig. 10. — The Black Drop, as olserA'ed by Bevis. 

this or that cause is the true one. It appears probable 
that the phenomenon is occasioned by the combina- 
tion of several causes^ and is widely variable in its 
extent. The general cause — by which I mean the 
resultant of the various causes in operation— is mani- 
estly an apparent extension of the sun's disc^ and an 
ipparent contraction of the disc of Venus. Suppose, 
for instance^ that the arc s s'v' (fig. 11) represents 
part of the true outline of the sun, then this outline 
appears shifted outside its true place, or to the position 
indicated by the boundary between light and shade in 
the figure ; and the apparent outline of Venus is shifted 



64 TRANSITS OF VENUS. 

from s'y y', its true position, to that shown by the out- 
line of the black disc. Supposing this shifting of the 
outline to be uniform, and to continue unchanged in 





Fig. 11. Fig. 12. 

Illustrating the Formation of the ' Black Drop.' 

extent, as Venus gradually passes on to the sun's face, 
it is clear that at the moment of true contact, when 
the real outlines touch, as shown in fig. 12, the ap- 
parent outlines will belong to two circles which are 
far from touching. But at the actual point of contact, 
where the widening of one outline and the contraction 
of the other cannot be supposed to act, there will still 
remain a fine black ligament. Under less perfect 
conditions this moment of true contact would not be 
attained, and instead of a fine ligament being seen 
just before Venus separated from the sun's edge, a 
wider ligament would be observed. 

Thus far I have only indicated the general cause. 
And it may be said that this general cause is demon- 
strated by the observed effects. But we must now 
consider how this general cause is itself brought about ; 
and herein lies the diflficulty of the matter, whether 
regarded as a problem or considered with reference to 
the practical mastery of this occasion of error. 



THE TRANSIT OF 1761. 65 

First, we have the rippling I have spoken of. 
Taking any point on the outline of the sun's disc or of 
Yenus's, that point is swayed backwards and forwards 
across its true position by the effect of atmospheric 
undulation^ the range of oscillation being greater 
or less according as the atmosphere is more or less 
perturbed^ and as the sun is observed nearer to or 
farther from the horizon. A moment's consideration 
will show that the effect of such oscillations^ operating 
all round both discs^ must be to cause the sun's disc 
to cover (on the whole) a larger space than it should^ 
while the disc of Venus covers a less space than it 
should. For there is a certain fringe of space all 
round both discs which is partially illuminated by 
these oscillatory movements^ and this partial illumi- 
nation extends the sun's disc outwards and contracts 
that of Venus. Probably this cause has but a small 
share in producing the general effect, except when the 
sun is low down. 

Secondly^ there is the optical effect caused by the 
fact that the image of a bright point is not itself a 
point. And here Ave have three causes in operation, 
which we may consider together. First, in the most 
perfect telescope the image of a point is Avhat is called 
the ^ circle of least confusion^ between the two linear 
(or almost linear) foci. Secondly, diffraction affects 
the dimensions of the focal image of a point of light. 
And thirdly, if the telescope is defective, spherical 
aberration may operate so as seriously to affect the 
definition. All these causes combine to alter the 

F 



66 TRANSITS OF VENUS, 

image of each point of the outlines of the sun and 
Venus into a small disc of light instead of a point. 
The result necessarily is that the outlines extend be- 
yond the true boundary of light and dark ; that is, the 
disc of the sun is enlarged and that of Venus is con- 
tracted. 

Thirdly^ there is a cause which might, perhaps, 
have been combined with the last — the qualities of the 
eye regarded as an optical instrument ; for the image 
of a point on the retina is not a point but a minute 
circle, even when the object is viewed directly. 

Fourthly J there is the effect called irradiation, by 
which the apparent size of a bright object is enlarged. 
This effect will be greater or less according as the 
contrast between the bright object and the dark back- 
ground on which it is projected is greater or less. 
Moreover, it appears that irradiation not only differs 
in amount wdth different observers, but varies even 
with the same observer at different times. Nay, its 
amount varies from moment to moment with the vary- 
ing mental effort made by the observer to ascertain, 
more or less exactly, the true outline of the observed 
object. 

We cannot wonder if the observations of the 
transit of 1761, affected as they were by peculiarities 
of appearance resulting from these various causes, for 
the operation of which observers were not on that 
occasion prepared, led to no trustworthy results. 



THE TRAXSIT OF 1769. 6/ 



CHAPTER III. 

THE TBAXSIT OF 1769. 

The general impression among astronomers^ after the 
observations of 1761 had been discussed^ was that too 
much reliance had been placed on Delisle's method. 
^ Experience/ wrote J. D. Cassini, later^ in his ^ His- 
toire da Passage de 1769/^ is our chief instructor; 
the fruit of its lessons indemnifies us for the value of 
the years they cost us. The principal end had been 
missed, in 1761, for want of observations in places 
where the durations differed sufficiently. It was 
essential not to experience a second time the same 
disadvantage.' 

Among the first statements published respecting 
the transit of 1769 was that by the ingenious Ferguson, 
who wrote as follows in 1762 : ^ On the 3rd of June, 
in the year 1769, Yenus will again pass over the sun's 
disc, in such a manner as to afford a much easier and 
better method of investigating the sun's parallax than 
her transit in the year 1761 has done. But no part 
of Britain will be proper for observing that transit,^ 

* This Tvas an error, due to Ferguson's reliance on Halleys tal-les ; 
not. I need hardly say, the taLles by vhich Halley had arrived at his 

F 2 



68 TRANSITS OF VENUS 

SO as to deduce anything with respect to the sun's 
parallax from it, because it will begin but a little 
before sunset^ and will be quite over before two o'clock 
next morning. The apparent time of conjunction of 
the sun and Venus^ according to Dr. Halley's tables^ 
will be at thirteen minutes past ten o'clock at London, 
at which time the geocentric latitude of Venus will 
be full ten minutes of a degree north from the sun's 
centre ; and therefore^ as seen from the northern 
parts of the earth, Venus will be considerably de- 
pressed by a parallax of latitude on the sun's disc ; 
on w^hich account the visible duration of the transit 
will be lengthened ; and in the southern parts of the 
earth she will be elevated by a parallax of latitude on 
the sun, which will shorten the visible duration of the 
transit with respect to its duration as supposed to be 
seen from the earth's centre ; to both which affections 
of duration the parallaxes of longitude will also con- 
spire. So that every advantage which Dr. Halley 
expected from the late transit will be found in this, 
without the least difficulty or embarrassment. It is, 
therefore, to be hoped that neither cost nor labour 
wall be spared in duly observing this transit, especially 
as there will not be such another opportunity again in 
less than 105 years afterwards.' 

Ferguson also showed accurately the places where 
advantage could be best taken of Halley's method : 
^ The most proper places for observing the transit in 

incorrect ideas respecting tlie cirenmstances of the earlier transit, but 
those which Halley had formed siibs.qnentlv. 



THE TEAXSIT OF 1769. 69 

the year 1769 are in the northern parts of Lapland, 
and the Solomon Isles in the Great South Sea, at the 
former of which the visible duration between the two 
internal contacts will be at least tAventy-two minutes 
o-reater than at the latter, even thouo^h the sun's 
parallax should not be quite 9'^ If it be 9^^ (which 
is the quantity I had assumed in a delineation of this 
transit which I gave in to the Royal Society before I 
had heard w^hat Mr. Short had made it from the 
observations of the late transit), the difference of the 
visible durations, as seen in Lapland and in the 
Solomon Isles, will be as expressed in that delineation; 
and if the sun's parallax be less than 9'^ (as I now 
have very good reason to believe it is) the difference 
of durations will be less accordingly.' 

Later, Hornsby in England, and De Lalande and 
Pingre in France, discussed very carefully the cir- 
cumstances of the transit of 1769. De Lalande, in 
1764, illustrated the conditions of the transit of 1769 
by a projection of the earth planned like that which 
Delisle had made for the transit of 1761. The 
tables of Cassini formed the basis of the calculations 
made by these astronomers ; and as Cassini had had 
the advantage of later observations of Venus, his 
tables were necessarily more accurate than those 
w^hich Halley had completed earlier in the century. 

The circumstances of the transit of 1769 in dif- 
ferent parts of the earth can be inferred from what is 
shown in Plate V. Here the arcs A i b and A^ i^ b' 
separate the dark and light hemispheres of the earth 



70 TRANSITS OF VEXUS. 

at the beginning of the transit, while the arcs c E D 
and c^ yJ d' separate the dark and light hemispheres 
at the end of the transit. Thus the beginning was 
visible at all places on the hemisphere formed by 
combining the sections A i e D and a' i' b^ d' ; and tlie 
end of the transit was visible at all places on the 
hemisphere formed by combining the sections ceda 
and c' E^ D^ a". The whole of the transit was visible 
over the spaces T>eix and T>^ m^ a! \ but within the 
space ime, though the beginning and end of the 
transit were seen, the progress of the transit was not 
wholly visible. Xo part of the transit was visible over 
the spaces b m c and b' i e^ c^ ; but within the space 
I m' e\ thouo;h neither the besfinnino; nor the end were 
visible, the progress of the transit was partially visible. 
At all points of the arcs a i b and a^ i^ b^ the ingress 
occurred with the sun on the horizon ; but whereas 
the sun was rising for the arcs A i and A^ i\ he was 
setting for the arcs JB i and B^ i\ At all points of the 
arcs c E D and c' E^ v> the egress occurred with the 
sun on the horizon ; but whereas the sun was rising 
for the arcs C e and c^ e\ he was setting for the arcs 
T> e and D^ e\ At the points m and m^ the sun was on 
the horizon both at ingress and at egress ; but whereas 
the whole transit, except ingress and egress, took place 
during the night at m^ it took place during the day at 
m\ All that has here been said has related to the 
passage of Venus's centre. 

The point i was that where ingress occurred 



THE TEAXSIT OF 1769. 



71 



earliest^^ tlie point i^ being that where ingress occurred 
latest. It was around these points that observers of 
ingress by Delisle's method were to be placed, on that 
side of the arcs A B and on A^ b' where the sun would 
be above the horizon at the time of ingress. We see 
that Great Britain was admirably placed for observing 
accelerated ingress, Greenwich being almost as well 
placed as any station could possibly be, though having 
the sun rather low (and unfortunately it appeared 
from Halley's tables as though the sun would be still 
lower). At Greenwich sunset was approaching when 
transit began, i^ was in a little known part of the 
Southern Seas. 

The point e", where egress occurred earliest, was, 
like i', placed in a part of the Southern Seas about 
which little was at that time known. E, where egress 
occurred latest, was so placed that the whole of 



^ Encke, in 1822, found the follo^ng elements for the transit of 

1769. I quote these, like the elements for 1761, from IM. Dubois' 
' Les Passages de Venus sur le disque Solaire ' : — 

h. m. s. 



Ingress of Venus' s centre . 


7 


26 


D^-b 


1 Green^nch 


Middle of the transit 


. 10 


27 


20-8 


J- apparent 


Egress of the centre 


. 13 


27 


ol-3 


J solar time. 


Duration of the transit 


. 6 





56-8 


- 


Least distance of centres . 


, 


10 


8-1 






Latitude 

/ 




Longitude 
/ 


Pole of accelerated ingress 


. 49 


S3X 




7 23 E 


,, „ retarded ,, . 


. 49 


33 S 




172 37 w 


,, 5, accelerated egress . 


. 22 


SOS 




122 46 W 


,, ,, retarded ;,- • 


22 


30 X 




o7 14E 


,, „ shortened durations 


. 38 


37 s 




143 2W 


,. ,, lengthened „ 


. 38 


37 X 




39 58E 



72 TRANSITS OF VENUS 

India and the region between the north-west of India 
and the Sea of Aral was suitable for observino; this 
phase. 

But chief interest was attached, as I have said, to 

the application of Halley's method. The Halleyan 

poles were at H and h^, these being respectively the 

points where, in a geometrical sense (that is, without 

taking into account the actual visibility of ingress 

or egress), the transit would be respectively most 

lengthened and most shortened. H, we see, lay in a 

region whence no part of the transit could be seen, 

and the point m was the nearest to H where both the 

beginning and end would be visible, but with the sun 

upon the horizon. The space i m e was that ^vhich 

presented the most promising conditions, except that 

the sun would be low within this space, both at ingress 

and at egress (passing below the horizon for a greater 

or less portion of the progress of the transit). Ward- 

huus, in Lapland, close to this region, was selected for 

the most northerly Halleyan stations ; and as the 

polar regions could not be occupied, the stations next 

in order of value were necessarily those lying on the 

opposite side of the arctic circle, from Kamschatka, 

through Alaska, &c., round to Hudson's Bay. These, 

however, were too far away from H to be of great 

value as Halleyan stations, while their great distance 

from I and E prevented them from having any special 

value as Delislean stations. The southern Halleyan 

pole H^ was in the same unknown quarter of the 

Southern Seas in which i! and E^ are seen to lie. In 



THE TRANSIT OF 1769. 73 

fact, the whole region around H^ was of extreme im- 
portance for the observation of the transit of 1769, 
since any station placed there would not only be 
excellent for Halley's method, but also for Delisle's, 
both as respects retarded ingress and accelerated 
egress. 

In passing, let it be noted how the superiority of 

the second transit of a pair (in general) shows itself 

by the positions of H and h^ in Plates IV. and V. 

respectively. In Plate IV. we see that H and m lie 

on opposite sides of the north pole, H^ and m^ on 

opposite sides of the south pole ; whereas in Plate V. 

we see that h and m are on the same side of the north 

pole, H^ and mf on the same side of the south pole. 

N0W5 necessarily one Halleyan pole lies in the region 

whence no part of the transit can be seen, and we see 

that in such a case as that illustrated by Plate V. the 

point m indicates how near that particular Halleyan 

pole H can be approached without losing either the 

beginning or end of the transit ; whereas in the case 

illustrated by Plate IV., m\ the point of nearest 

available approach, lies very much farther away from 

the corresponding Halleyan pole H^ Still, it is to be 

noticed that, even in the case of a transit like that of 

1769 (Plate V.), the really effective use of Halley's 

method requires that a station should be reached near 

the space corresponding to e m i. If this cannot be 

arranged, the stations next in order of value are those 

lying on the farther side of the arctic or antarctic 

circle (as the case may be), and such stations will 



74 TRANSITS OF VENUS. 

commonly not be much better than one near m! for 
the transit of 1761 (Plate IV.), and may be even far 
inferior to stations available in the case of such a 
first transit as that of 1874 (Plate VI.). This is, in 
fact, the reason why Halley's method fails totally in 
1882 (see Plate VIL), though this is the second 
transit of a pair. 

The actual operations for viewing the transit of 
1769 were carried out on a widely extended scale. 
Preparations were made for sending observers to the 
South Sea, California, Mexico, Lapland and Kams- 
chatka. The King of Denmark invited Father Hell, 
the eminent German astronomer, to observe the transit 
at Wardhuus, in Lapland, and thither Hell betook 
himself with Borgrewing, the Danish astronomer. 
They arrived in the autumn of 1768, and passed the 
winter in that desolate region. Chappe d'Auteroche 
Avas selected by the French Academy to observe the 
transit from the Solomon Isles, in the South Sea ; but, 
says M. Dubois, ' the South Sea at that epoch was 
under the rule of Spain, and it was only possible to 
visit those seas in a Spanish vessel, and with the 
permission of the Court of Spain. The Spanish 
Government refused such permission, but gave Chappe 
leave to embark in the Spanish fleet then about to 
sail for Western America.' Chappe eventually ob- 
served at St. Joseph, in California. 

^ England,' says M. Dubois, ^ did not wait for 
permission from Spain to send an astronomer to ob- 
serve the transit from the South Sea.' The folio wins; 



THE TRANSIT OF 1769. 75 

nccount^ taken from ^ Cook's Voyages,' describes the 
preparations made for the journey : — 

' It having been long before calculated that the 
planet Venus would pass over the sun's disc in 1769, 
a phenomenon of great importance to astronomy, and 
which had eno^as^ed the attention of men of science, it 
was judged that the most proper place for observing 
this phenomenon would be either at the Marquesas 
or at one of those islands to which Tasman had given 
the several appellations of Amsterdam, Rotterdam, and 
Middleburg, but which are now better known under 
the general name of the Friendly Islands. This 
being a matter of so much importance in the science 
of astronomy, the Royal Society, with that laudable 
zeal they have ever shown for its advancement, pre- 
sented a memorial to his Majesty at the beginning of 
the previous year, requesting among other things that 
a vessel might be fitted out, a.t the expense of the 
Government, to convey proper persons to observe this 
transit at one of the places already mentioned. The 
petition being readily complied* with, and orders 
having been given by the Admiralty to provide a 
vessel for that purpose, on April 3, Mr. Stephens, 
the Secretary to the Board, informed the Society that 
everything was progressing according to their wishes. 

'^ Mr. Dalrymple was originally fixed upon to 
superintend this expedition : a man eminent in science, 
a member of the Royal Society, and who had already 
greatly distinguished himself respecting the geography 
of the Southern Ocean. As this o-entleman had been 



^^ TRANSITS OF VEXUS. 

regularly bred to the sea, he insisted (very properly 
too) on having a brevet commission, as captain of the 
vessel, before he would undertake the employment. 
Sir Edward Hawke (afterwards Lord Hawke, a naval 
officer, and not a civilian), who then presided at the 
Admiralty, violently opposed this measure ; and being 
pressed on the subject, declared that nothing would 
induce him to give his sanction to such a commission. 

' Both parties were inflexible, and it was therefore 
thought expedient to look out for some other person 
to conduct the expedition. Accordingly, Mr. Stephens, 
having recommended Lieutenant Cook, and this re- 
commendation havino; been streno^thened bv the testi- 
mony of Sir Hugh Palliser, who was well acquainted 
with Cook's merit and abilities for the discharge of 
this office, he was appointed to this distinguished post 
by the Lords Commissioners, and promoted to the rank 
of Lieutenant of the Royal Is^avy on May 25, 1768. 
He was now, be it remembered, close upon forty years 
of age. 

^ This appointment having taken place, Sir Hugh 
Palliser was commissioned to provide a vessel adapted 
for such a voyage. After examining a great number 
then lying in the Thames, in conjunction with Cook, 
of whose judgment he entertained the highest opinion, 
they at last fixed upon the ^Endeavour,' a barque of 370 
tons, which had been built for the coal-trade. 

' In the interim. Captain AVallis having returned 
from his voyage round the world, and having signified 
to the Eoyal Society that Port Royal Harbour, in 



THE TRAXSIT OF 1769. 77 

King George's Island, now called Otalieite, would be 
the most convenient place for observing the transit, 
his opinion was adopted, and the observers were ordered 
to repair thither. 

' Mr. Charles Green, the coadjutor of Dr. Bradley, 
the Astronomer Royal, was nominated to assist Captain 
Cook in conducting the astronomical part of the un- 
dertaking ; and he was accompanied also by Joseph 
Banks, Esq. (afterwards Sir Joseph, the President of 
the Royal Society). This friend of science possessed 
at an early period of life an opulent fortune, and 
being zealous to apply it to the best ends, embarked 
on this tedious and hazardous enterprise, animated 
by the wish of improving himself and enlarging the 
bounds of knoAvledge. He took two draughtsmen with 
him, and had likewise a secretary and four servants in 
his retinue. 

' Dr. Solander, an ingenious and learned Swede, 
who had been appointed one of the librarians in the 
British Museum, and w^ho was particularly skilled as 
a disciple of Linnceus, and distinguished in his know- 
ledge of natural history, likewise joined the expedition. 
Possessed with the enthusiasm with which Linn^us 
inspired his disciples, he braved danger in the prose- 
cution of his favourite studies ; and being a man of 
erudition and capability, he added no small eclat to the 
voyage in which he had embarked. 

^ Though the principal intention of this expedition 
was to observe the transit of Venus, it was thought 
proper to comprehend other objects as well. Captain 



78 TRANSITS OF VEX US. 

Cook was therefore directed^ after he had accomplishec 
his main business^ to proceed in making further dis 
coveries in the South Seas^ which now began to be 
explored with uncommon resolution.' 

The expedition sailed from Deptford on July 30, 
1768^ and on August 13 anchored in Plymouth Sound, 
from which after a few days' stay they proceeded to 
sea. It was not until April 10 that they saw Otaheite. 
' On the 10th/ says the narrative, ^ upon their looking 
out for the island to which they were destined they 
saw land ahead. The next morning it appeared very 
high and mountainous, and it was known to be King 
George the Third's Island, so named by Captain AVallis, 
but by the natives called Otaheite.' 

. In May they ^ began to make preparations for 
observing the transit of Venus ; and from the hints 
which Captain Cook had received from the Royal 
Society, he sent out two parties to make observations 
from different spots, that in case they failed at Otaheite 
they might succeed elsewhere. They employed them- 
selves in preparing their instruments, and giving in- 
structions in the use of them. On Thursday, June 1 
(the next Saturday being the day of the transit), they 
sent the long-boat to Eimayo, having on board Mr. 
Gore, Mr. Monkhouse, and Mr. Sporing, a friend of 
Mr. Banks, each furnished with necessary instruments 
by Mr. Green. Mr. Banks and several of the Indians 
w^ent out with this party. Others were despatched to 
find out a convenient spot at such a distance from 
their principal station as might suit their purpose. 



THE TEAXSIT OF 1769. 79 

Those who went to Eimayo in the long-boat, after 
rowing the best part of the night, by the help of some 
Indians on board a canoe which they hailed, fonnd a 
proper situation for their observatory upon a rock, 
where they fixed their tents, and prepared the apparatus 
for the following day's observation. On Saturday, 
June 3, as soon as it was light, Mr. Banks left them 
to go to the island for fresh provisions. As he was 
trading with the natives who belonged to Tarras the 
king of the island arrived, with his sister, whose name 
was Nuna, in order to pay him a visit. . . . Mr. 
Banks returned to the observatory with his visitors, 
and showed them the transit of the planet Venus over 
the sun's disc, informing them that he and his com- 
panions had come from their own country solely to 
view it in that situation. Both the parties which were 
sent out made their observations with great success. 
They nevertheless differed in the accounts of the times 
of transits more than might have been imagined.' In 
Captain Cook's journal, the following account is 
given : ^ The day proved as favourable to our purpose 
as we could wish ; not a cloud was to be seen the 
whole day, and the air was perfectly clear ; so that we 
had every advantage in observing the Avhole of the 
passage of the planet Venus over the sun's disc. ^Ve 
very distinctly saw an atmosphere, or dusky shade, 
round the body of the planet, which very much dis- 
turbed the times of the contact, particularly the two 
internal ones. It was nearly calm, the whole day, and 
the thermometer, exposed to the sun about the middle 



80 TRANSITS OF VENUS. 

of the day^ rose to a degree of heat we have not before 
met with.' 

Chappe was specially fortunate at St. Joseph. His 
observation has given rise to a good deal of controversy, 
wdth regard to its bearing on the question of the solar 
parallax. Powalky and others consider that Chappe's 
observation of the internal contact at egress was an 
observation of real contact, not apparent contact; Stone 
maintains the contrary. My attention was specially 
directed to this point by Newcomb, of Washington, 
U.S., and I must confess that Chappe's narrative 
seems to me unquestionably to bear the interpretation 
given to it by Powalky, with whom Xewcomb agrees. 
Let the reader judge, remembering that real contact 
means the formation of the black drop or of the pear- 
shaped figure described at page 57 ; so that at total 
ingress real contact is later than apparent, while the re- 
verse is the case at egress. Chappe writes as follows : — 
^ At the total ingress I observed very distinctly the 
second phenomenon, which had been noticed by the 
greater part of the observers in 1761. The edge of 
the disc of Venus lengthened itself, as if it had been 
attracted by the sun. I did not observe, for the instant 
of total ingress, the instant when the edge of Venus 
commenced to extend itself; but, not being able to 
doubt that this black point was not part of the opaque 
body of Venus, I observed the moment when it ended 
(/ ou il etait a sa fin ') in such sort that the total 
ingress could not have occurred earlier, though perhaps 
later by t^vo or three seconds. The black point was 



THE TRANSIT OF 1769. 8 1 

a little less dark than the rest of Venus ; I think it 
is the same phenomenon which I had observed at 
Tobolsk in 1761. ... At the second internal con- 
tact' (that is, internal contact at egress), ^the sun Avas 
undulating, as was Venus also, which rendered the 
observation very difficult. At this contact Venus elon- 
gated herself more considerably than in the morning, 
in approaching suddenly the edge of the sun.' It 
seems clear that Chappe here witnessed that sudden 
leap to the sun's edge at egress which is the counter- 
part of the sudden leap from the sun's edge at ingress ; 
and that if the contact differed at all from the con- 
tact at ingress, it was in the fact that a longer leap 
was made, in other words, that he caught an earlier 
phase at ingress, which would correspond of course to 
a later phase at egress. As Chappe says himself that 
real contact at ino;ress mio;ht have been two or three 
seconds later, but certainly not earlier, we see that the 
contact he observed at egress corresponded even more 
closely with what he regarded as real contact, — that is, 
the moment of the leap by which the black drop is 
formed and broken. Yet Mr. Stone considers that 
at egress Chappe missed the real contact and observed 
the later phase of apparent contact.^ 

Le Grentil experienced in 1769 the culmination of 

^ Here and at pp. 90-92, 1 retract the views I expressed iu my ' Sun,' 
and in reply to Prof. Newcomb's general criticism on my account of 
Stone's work. So soon as we met, and he described bis objections in 
detail, I recognised their force. The Astronomical Society had, in fact, 
pronounced so decisively in favour of Stone's treatment of the transit of 
1769, that I was not prepared to find errors so serious in it. 



82 TRANSITS OF VEXUS. 

his misfortunes. With a persistent courage worthy of 
better success he determined, after his failure in 1761, 
to return to Pondicherry as soon as an opportunity 
presented itself, and to aAvait there during eight years 
the transit of 1769. Dubois remarks that Le Gentil 
usefully employed those years in studying the astro- 
nomy of the Brahmins, on which subject he published 
an interesting work upon his return to France. But 
the object he had specially in view was unfortunately 
not attained. ' On June 3, 1769,' says Dubois, ^at the 
moment when this indefatigable observer was preparing 
to observe the transit, a vexatious cloud covered the 
sun, and caused the unhappy Le Gentil to lose the fruit 
of his patience and of his efforts.' Pondicherry would 
have been a useful station for observing the retarded 
egress, as we see from Plate V. 

Pingre, who had observed the transit of 1761 at 
Rodriguez, was sent to observe the transit from a 
French station in the island of St. Domingo. 

Although the observations made in 1769 were on 
the whole much more satisfactory than those which had 
been made in 1761, yet there was much to throw doubt 
on any determination of the sun's distance based even 
on the later transit. \Ye have seen already that the 
peculiar distortion of Venus, illustrated in pp. 61-63 
was presented in a marked degree in 1769; but even 
more unpromising was the observed difference in time 
between the moments of real and apparent contact. It 
is only necessary, as M. Dubois points out, to consider 
the difference recognised by those observers who noted 



THE TRAXSIT OF 1769. 83 

the two phases, to see how largely the accuracy of 
the deduced solar distance must be affected by this 
cause. 

Wales, at Hudson's Bay, using a telescope two 
feet long, magnifying 120 times, found a difference 
of 24 seconds between the real and apparent contacts 
at egress. Green, at Otaheite, found a difference of 
40 seconds at ingress and 48 seconds at egress. Cook, 
at the same station, found the difference 60 seconds at 
ingress and 32 seconds at egress. Yet these two 
observers used two similar telescopes, magnifying 140 
times. Maskelyne, at GreeuAvich, using a telescope 
magnifying 140 times, found the difference 52 seconds ; 
while Horsley, at the same station, with an achromatic 
telescope, 10 ieet in length, magnifying 50 times, found 
the difference to be 63 seconds. Maskelyne remarks 
that the difference was greater than he had expected, 
considering that the telescopes were all nearly of the 
same quality, except a reHector of six feet used by 
Hitchins. The superiority of this instrument ap- 
peared to Maskelyne to account for the difference of 
26 seconds, by which interval Hitchins observed the 
internal contact earlier than Maskelyne. Hornsby, at 
Oxford, used an achromatic telescope of 7^ feet, magni- 
fying ninety times, and found the difference to be 57 J 
seconds; while Schuckberg, also observing at Oxford, 
found a difference of 69 seconds between the real and 
apparent contacts. An unknown observer at Caen, 
using a very small telescope, found the enormous dif- 
ference of fully 150 seconds! Wilke, at Stockholm, 

G 2 



84 TRANSITS OF VENUS. 

also using a very small telescope, estimated the dif- 
ference at 43 seconds. Lastly, Euler, observing at 
Orsk, with a telescope 12 feet in leijgth, noted for the 
instants of contact two epochs differing by 50 seconds. 
When we consider these wide and widely varying dif- 
ferences among observers who observed both kinds of 
contacts, we cannot wonder if considerable differences 
of absolute time were noted between observations of 
the same contact by different observers either at the 
same stations or at stations near enouo;h for institutintir 
a comparison. Thus, Le Monnier and De Chabert, at 
St. Hubert, noted instances of contact differing 36 
seconds from each other ; while between Duval le Roy 
and De Verdun, at Brest, there was a difference of 30 
seconds. 

It is well remarked by Dubois that observations of 
external contact at ingress can have no value. He adds 
that observations of external contact at egress are 
somewhat more reliable ; but it must be very dif- 
ficult to distinguish the moment when the solar limb 
resumes an exactly circular shape. Accordingly the 
fourteen exterior contacts noted by different ob- 
servers could have no real value. Yet it is worthy 
of remark that the difference between moments of ex- 
ternal contact observed at St. Petersburg by Mayer 
and Stahl amounted only to 27 seconds ; while at 
Gurief the difference between two such observations 
amounted to 28 seconds. So that, as Newcomb has 
remarked of the observations made during the transit 
of Mercury in November 1868, it would seem as 



THE TRANSIT OF 1769. 85 

though the errors In the estimated instant of an ex- 
ternal contact might be expected to be of the same 
order as those affecting the estimated instant of an 
internal contact. 

Dubois tells us that upwards of two hundred 
memoirs were sent to the Academy of Sciences on the 
value of the solar parallax deducible from the obser- 
vations made in 1769. How many were sent to the 
Royal Society I do not know ; but probably as many 
as four hundred were sent to the different learned 
bodies of Europe. 

A comparison of the results obtained by the most 
competent computers showed that the observations of 
1769 were much more valuable on the whole than 
those of 1761 ; for, whereas the results obtained in 1761 
ranged in value between 8^^*5 and 10'^-6, we find the 
following five results selected as those most carefully 
calculated on the basis of the observations of 1769 : — 

De Lalande fixed the parallax at 8*50 
Fr. Hell ,, ,, 8-70 

Hornsby „ ,, 8*78 

Euler „ ,, 8-82 

Pingre ,, „ 8-88 

The solar distances corresponding to the parallaxes 
8''-50 and 8''-88 are respectively 96,162,840 miles 
and 92,049,650 miles. 

It is somewhat singular that, notwithstanding the 
clearest evidence of a cause of uncertainty sufficing to 
account for such differences as the above table presents, 



86 TRAXSITS OF VEXUS. 

Lalande and Pingre, who had obtained the most widely 
different results, were both quite confident of the 
accuracy of the values they had deduced. Lalande 
says in his memoir, that regarding the whole series of 
observations of 1769, the solar parallax is in^'ontestably 
8^^*5 ; while Pingre says in reply, ^ of two things one : 
either no result at all can be deduced from the transit 
of 1769, or it must be admitted that the value of the 
solar parallax is very close indeed to 8'^'8 (^ est a tres- 
peu pres de 8''-8).' 

In his first memoir, in which the above tabulated 
value, 8^^*82, was given, Euler had not taken into 
account the observations made at Otaheite by Green, 
and at St. Joseph, in California, by Chappe. Going 
over his work afresh, and introducing these observa- 
tions, he deduced the parallax 8'^*68. Dionis du Sejour, 
employing only observations of duration, and combining 
the transits of 1761 and 1769, deduced the value 8'^*84. 
But in his ^ Traite Analytique des Mouvements 
Apparents des Corps Celestes ' he adopts as the final 
result of his calculations the solar parallax 8^^*8128. 

It is worthy of notice that when chief reliance was 
placed on observations made at Halleyan stations of 
the first class, the value of the parallax approached 
more nearly to that now recognised as probably the 
more correct. Thus, combining observations made at 
Otaheite with Father Hell's observations at Wardhuus, 
De Lalande obtained the value 8'^'72, and yet larger 
values when Hell's observations were combined with 
other observations. Yet, as we have seen, De Lalande 



THE TRANSIT OF 1769. 8/ 

adopted S^^'o as the best mean value of the solar 
parallax. 

Doubts^ indeed, were thrown upon Father Hell's 
observations, on account of corrections which had 
been made in his MS. notes of the phenomena (and 
partly, also, because of the known fact that he alone of 
all the observers of the transit recognised no distinc- 
tion between real and apparent contacts). The idea 
that Hell's records were forged was thrown out by 
the Astronomer Royal. But such a suspicion need 
hardly be seriously considered. Not only is nothing 
known about Fr. Hell which for a moment justifies 
the supposition that he could be guilty of the act 
charged to him, but we know now that his observations 
accord better with the latest estimates of the parallax 
than those of other observers. 

Encke in 1824 published an analysis of the observa- 
tions of the transit of 1769, from which he deduced for 
the solar parallax the value 8'^*6030. By combining 
the observations of both transits he deduced that value 
8'^-5776 (corresponding to a solar distance of 95,274,000 
miles) which for more than a quarter of a century 
thereafter maintained its ground in treatises on astro- 
nomy. 

But about the year 1850 it began to be recognised 
that the sun's distance had been over-estimated. 
Various methods of determining the solar parallax, 
inferior singly to the observation of transits of 
Venus, but collectively superior — and superior, more- 
over, because of the greater accuracy with which 



88 TRANSITS OF VENVS. 

(owing to the improvement in instruments of precision) 
they could be applied — concurred in showing that the 
sun's distance was less than had been supposed by at 
least three millions of miles. The consideration of 
these methods in detail would occupy more space than 
is here convenient. The reader will find them fully 
described in the second chapter of my treatise on the 
sun. In this place let the following summary 
suffice : — 

In 1845 Hansen announced that by a method 
based on observations of the moon's motions he had 
deduced the parallax 8^^*9159, corresponding to a dis- 
tance of 91^659^000 miles. Leverrier, from the care- 
ful study of the sun's apparent motions, as affected by 
the earth's monthly revolution around the common 
centre of gra\dty of herself and the moon, deduced a 
solar parallax of 8^^*95, corresponding to a distance of 
91,330,000 miles. Prof. Newcomb, of Washington, 
U.S., obtained by the same method the parallax 8^^*84, 
distance 92,500,000 miles. From observations of 
Mars when at his nearest to the earth Prof. Newcomb 
deduced the parallax 8^^*85, corresponding to a distance 
of 92,300,000 miles. Stone, formerly of Greenwich, 
obtained by this method the distance 91,400,000 miles; 
w^hile Winnecke deduced the distance 91,200,000 miles. 
Foucault, measuring the velocity of light by means of 
a rapidly revolving mirror (a plan devised by AVheat- 
stone), and comparing the value so obtained with that 
inferred from the observation of the eclipses of Jupiter's 
satellites and the aberration of lio-ht, deduced the solar 



THE TEANSIT OF 1769. 89 

parallax 8^^*86, corresponding to a distance of 
92,100,000 miles. From the study of tliose planetary • 
perturbations TN'hich depend on the relative masses of 
the earth and the other planets Leverrier deduced the 
value 8''-859 for the parallax, or 92,110,000 miles for 
the sun's distance. It will be seen that the values 
thus obtained indicate a solar parallax of 8^^*89, corre- 
sponding to a distance of about 91,950,000 miles. The 
limits of probable error are considerable, however, 
and we scarcely know more at present than that the 
solar parallax almost certainly lies between the values 
8'^*82 and 8'^-96, corresponding to the distances 
52,676,000 miles and 91,228,000 miles. 

As soon as it became clearly recognised that 
Encke's estimate of the sun's distance from observa- 
tions of the transit of 1769 was considerably in error, 
doubt necessarily fell upon the method itself which 
had till then been regarded as the most satisfactory for 
determining the sun's distance. Efforts, however, were 
made to restore the credit of the method by a re-ex- 
amination of the observations made in 1769. These 
eiforts have been regarded by many, especially in 
this country, as successful ; but it must be con- 
fessed the investigation has shown us rather how the 
error crept in than how it can be avoided in future 
applications of the method. This will appear when 
we consider the nature of the researches by which 
astronomers have sought to restore the waning credit 
of the observations of 1769. 

Powalky in 1864 discussed forty-four observations. 



90 TRANSITS OF VENUS, 

made at nineteen stations, the latitude of which seemed 
*to him satisfactorily determined. He dismissed seven- 
teen of these observations, and treated six of the re- 
maining twenty-seven as of inferior worth, giving to 
them only half the weight assigned to the other twenty- 
one. The observations thus retained were made at 
only thirteen stations. Amongst the observations 
were nine external contacts, four at ingress and five 
at egress. Powalky gives no sufficient reason for some 
of the selections made by him (between conflicting ob- 
servations made at stations in the same regions), nor 
for reo^ardino; as real contacts some observations which 
were not described with sufficient exactness to justify 
that interpretation. On the whole, it seems impossible 
to regard his conclusion as satisfactorily established. 
All he can be said to have proved is that amongst the 
observations made in 1769 it is possible to select several 
which, when combined, give a value of the solar paral- 
lax according fairly with the estimate recently adopted 
in preference to Encke's. 

The investigation published by Mr. Stone, of 
Greenwich, in 1868, has been regarded as more trust- 
worthy ; but it does not appear that those who have 
expressed approval of it had critically examined his 
memoir on the subject. When Sir John Herschel de- 
scribed Stone's work as removing the reproach from 
astronomy which had fallen upon the science in conse- 
quence of the large error detected in the estimate of the 
sun's distance, he appears to have taken Stone's results 
for granted, and not only so, but to have mistaken 



THE TRANSIT OF 1769. 9 1 

their real significanoe. I followed him in my treatise 
on the sun^ being partly influenced by the fact that 
the Astronomical Society had adopted Stone's con- 
clusions. But my attention having been directed by 
Professor Xewcomb, of America, to the slightness of 
the examination given to Stone's memoir by those 
^vho had accepted its results, I have been led to ex- 
amine it for myself, and I am obliged to admit that it 
has much less weight than some in this country have 
supposed. 

What Stone has done has been simply this. He 
has endeavoured (as others had done) to ascertain, 
from the account given by each observer, whether real 
or apparent contact was observed. And he introduced 
in the equations of condition a constant correction 
(seventeen seconds) for the diiference in time between 
the two contacts. Now, this constant is inferred from 
the equations themselves whence the parallax deduced 
by Stone, 8^^*91, is obtained; and his analysis really 
amounts to the distribution of the disposable errors 
affecting the observations of contact, in such sort 
that a part goes to change the parallax from Encke's 
value to 8'^-91, and the remainder to form the constant 
correction between real and apparent contacts. This 
would render the result unreliable,, even if we had 
reason to believe that the correct time-difference be- 
tween real and apparent contacts in any given transit 
really had a nearly constant value, and that value not 
far from seventeen seconds. Knowing as we do from 
the accounts of the observers themselves that the differ- 



92 TRANSITS OF VENUS, 

^nce varied greatly with the varying circumstances 
under which the observations were made, and always 
largely exceeded seventeen seconds^ it seems quite im- 
possible to adopt Mr. Stone's method as trustworthy. 
We cannot, therefore, wonder that Continental and 
American astronomers have, by common consent, de- 
clined to accept Mr. Stone's results as having much 
weight, or indeed as proving anything except what 
had already been ascertained — the fact, namely, that 
the observations made in 1769 afford but unsatisfac- 
tory evidence respecting the sun's distance. 

But the imperfect nature of the observations made 
in 1761 and 1769 can be sufficiently explained with- 
out attributing inferiority to the method of determin- 
ing the sun's distance in pursuance of which the 
observations were made. It cannot be doubted that 
the measurement of the sun's distance resulting from 
those observations was more trustworthy than any 
which could have been obtained at that time by other 
methods. We have learned to apply other methods 
so much more accurately than they could have been 
applied in the last century, that they give better results 
than a superior method could then give. But it still 
remains probable that the method depending on the 
observation of Venus in transit is superior to other 
modes of determining the sun's distance ; and that when 
this method is applied with the improved instruments 
of our time its superiority will be rendered manifest. 



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OF TRAXSITS AXD THEIR COXDITIOyS. 93 



CHAPTER IV. 

OF TRAXSITS AXD THEIR COXDITIOXS. 

Before we proceed to the consideration of the transits 
now approaching it will be desirable to enter on a 
more complete examination than heretofore of the 
general principles on which the determination of the 
sun's distance by observation of Venus in transit de- 
pends. To this subject the present chapter is there- 
fore given. It deals with the various methods which 
are available for determining the sun's distance^ the 
order in which transits recur^ and lastly^ the considera- 
tions on which the choice of stations will depend, in 
any given transit. These various points I wish to 
treat in an entirely popular manner, and therefore I 
shall leave out of account all those minor details 
which have to be considered in the complete discus- 
sion of the subject^ referring the reader who may 
wish for a more thorouo^h investio-ation of the matter 
to my ^Essays on Astronomy' and ^ The Universe 
and the Coming Transits.' 

Firsts then, let us consider the passage of Venus 
between the earth and the sun on the occasion of a 
transit, and see how the sun's distance may be inferred 



94 THAXSITS OF VFXUS. 

from the various appearances presented when the transit 
is viewed from different parts of the earth. 

Let E E^ (fig. 13; be the earth, and v Venus passing 
between the earth and the sun (at s) on the course 




Fig. 13. — Illustrating the general principles on which the determination 
of the Sun's distance by transit observation depends. 

shown by the arrow, so that at the moment Indicated 
by the figure a transit is in progress. At this moment 
let us suppose that from a northern station e^ Venus 
is seen projected upon the sun's face at v\ while from 
a southern station E she is projected at v {v and v' 
marking the place of her centre). It is to be noted 
that true perspective being quite out of the question; 
I here for convenience suppose the circle S to represent 
the disc of the sun seen from E, so that in considering 
what foUow^s the reader need not trouble himself about 
the curved nature of the sun's surface, 

Now^5 the proportions of the solar system being well 
known ever since the Copernican theory was established 
— or rather, since Kepler's laws were discovered — we 
know^ that the distance of v from the sun bears to the 
distance of E from the sun the proportion of about 72 
to 100 ; w^hence, immediately, w^e see that E Y bears to 
V V the proportion of about 28 to 72, or 7 to 18. And 
manifestly the opening-out of the lines Y e and Y E^ 
at the earth is less than their opening- out at the sun 



OF TRANSITS AND THEIR CONDITIONS, 95 

in this same proportion of 7 to 18 ; so that, for instance, 
if the two stations E and E^ are 7,000 miles apart 
(meaning the distance in a straight line, and for sim- 
plicity assuming that Y E and V E^ are equal lines sym- 
metrically placed with respect to the earth's globe), then 
i; vMs a distance of 18,000 miles. But such a deter- 
mination as this, if justly and s.atisfactorily made, would 
in point of fact amount to a determination of the sun's 
size, and therefore of the sun's distance. Observe — 
the astronomer at E is supposed to have accurately 
determined the apparent position of Venus's centre at 
V, while the astronomer at E^ has accurately determined 
the apparent position of her centre at v^ ; thus they 
know what proportion v v^ bears to the diameter of 
the disc S, that is, to the sun's diameter. Say, for 
instance, they find it to be the 47th part of this dia- 
meter. But they know also that v v is 18,000 miles 
in length. So that the sun's diameter is 47 times 
18,000 miles, or 846,000 miles. 

So soon, however, as we know the real size of the 
sun we know his distance. We know how large he 
looks, and a globe of given size can only present a 
certain apparent size at a certain distance. For ex- 
ample, a globe one inch in diameter looks just as large 
as the sun at a distance of about 107^ inches, or a 
little less than 9 feet ; ^ a s:lobe two inches in diameter 



^ A halfpenny, wliicli has a diameter of one inch, will be found to 
exactly conceal the sun when placed at a distance of 107^ inches, the 
sun being at about his mean distance — that is, the observation being 
made in March, April, September, or October. 



96 thaxsits of venvs, 

must be set tAvice as far away to look just as large as 
the sun ; a globe three inches in diameter thrice as far 
away ; and so on. In brief, the sun (like any one of 
these globes w^hen placed as described) lies at a dis- 
tance 107^ times as great as his own diameter. So 
that multiplying 846,000 by 107^ we get for the sun's 
distance (as resulting from the observations imagined 
above) 90,160,000 miles. , 

The considerations just discussed form the basis 
of all the various methods for determining the sun's 
distance by transit observations. These methods are 
only so many contrivances for bringing out the true 
result as satisfactorily as possible, by eliminating the 
various possible sources of error. 

We may call the method just sketched the direct 
method, because it depends on the simple observation 
of the place of Venus on the sun's face. I shall have 
occasion presently to discuss the method somewhat 
more in detail. Let it suffice, here, to notice that 
the method presents manifest difficulties. The two 
observers, at E and E^, are of course not in direct com- 
munication ; yet it is essential that their observations 
should either be made exactly at the same time or that 
at least the exact difference of time should be known. 
Again, it is not an easy matter to measure the place 
of Venus on the sun's face with the accuracy that the 
method requires. For these reasons Halley was led, 
in anticipation of the transit of 1761, to devise another 
method. 

Let us suppose, for simplicity, that the two stations 



OF TRANSITS AND THEIR COXDITIOXS 9/ 

at E and E^ are not shifted by the earth's rotation while 
the transit lasts. In this case the observer at E would 
see Yenus traverse such a path as Z v m^ while the 
observer at e' would see her traverse the parallel path 
r v^ m\ The time occupied by Venus in each case 
would of course be proportional to the apparent length 
of the lines I m and T m^ ; so that if the time were 
accurately noted by the two observers^ the apparent 
lengths of these lines would be known ; whence^ of 
course, the simplest possible geometrical considerations 
would give the position of the two chords and the ap- 
parent distance v v separating them from each other. 
This known, the sun's size and distance follow as in 
the direct method. Since the moment when Venus has 
just made her complete entry on the sun's face at in- 
gress, and is just about to begin to leave his face at 
egress (in other words, the moments when her disc 
just touches the sun's edge on the inside), were sup- 
posed by Halley to be determinable with great ac- 
curacy, such a method as has just been described 
seemed to him admirably adapted for determining the 
sun's distance. 

But clearly the difference of time in the imaginary 
case we have been dealing with, where the earth's rota- 
tion was neglected, will depend on the position of the 
chord of transit. Supposing Venus to traverse the centre 
of the sun's face, the two chords being equal in length, 
there would be no difference of time, while the differ- 
ence would be great if the two chords were near the 
edge of the disc. In the latter case the method would 

H 



98 TRANSITS OF VENUS. 

be most successfully applicable, while in the former 
it would not be applicable at all. Now, we have ^een 
that the transit of 1761, as calculated by Halley (see 
pp. 34 and 35), Avas nearly central. Xevertheless, 
owing to the rotation of the earth, a difference of dura- 
tion would occur in the case of such a transit. In a 
general way this has been already shown in the note 
on pp, 34 and 35. But it is also easy to show that a 
displacement comparable with the vv of fig- 13 can 
be inferred from time observations applit^d as Halley 
suggested for the supposed conditions of the transit of 
1761. 

Let us suppose that in fig. 14 we are looking down 
upon the earth e and Venus v from the north, Venus 




Yi-y, 1-i. — liiutetmcmg tlie eitect of the Earth's roLation ou the motion of 
Venus in transit. 

travelling (with respect to the earth) ^ in the direction 
shown by the arrow. Let us suppose i E to represent 
a chord of transit across the face of the sun s. Xow, 
the earth is rotating in the direction ic e e along 
the arc ic e ; and as a transit may last several hours, 

^ It is generally convenient to suppose the earth at rest, and Venus 
trarelling only with the excess of her ^notion over the earth's motion 
around the sun. 



OF THAXSITS AXD THEIR COXDITIOXS, 99 

a place Avhich was at w when transit began (that 
is, when Venus appeared to be at i) would be carried 
by rotation to some point e by the time the transit 
ended (that is, when Venus appeared to be at e). 
In order to see the effect of such a rotation-shift on 
the apparent motion of Venus, let us take two lines, 
one from iv^ the other from e, through the centre of 
Venus (supposed at rest at v, near the middle of the 
transit) to the chord I E ; we see that the line from 
he earlier position w passes to v, while the line from 
the later position e passes to v\ Thus the effect of the 
rotation of the earth during the time of transit, if con- 
sidered alone, corresponds to a shifting forwards of 
Venus by the amount v v\ In other words, transit is 
shortened by the effect of rotation in direction ic e. 
Suppose now another observer placed at the pole 
(whichever pole happened to be m sunlight at the 
time), so as not to be at all affected by rotation ; or 
that, being placed near either pole, he were much less 
affected by rotation ; or that, being placed on the side 
of the pole farthest from e w, the duration were 
lengthened through the effects of duration, instead of 
being shortened. Then there would arise on this ac- 
count a difference of duration, which would lead to 
the determination of the sun's distance precisely as in 
the case before supposed. For in reality the result 
would be the determination of the apparent amount of 
the displacement v v^ along the chord of transit, corre- 
sponding to the known displacement ic e upon the earth ; 
and the mere fact that both displacements are in an 

H 2 



lOO TRAXSITS OF VEXVS. • 

east-and-west direction does not render the observa- 
tions less eflfective than those which in the former case 
oave the apparent displacement v v corresponding to 
the observers' displacement E E^^ both displacements 
being on a north-and-sonth line. 

In all ordinary cases, Halley's method depends 
partly on the distance of the observers measured in a 
north-and-south direction, and partly on the effect of 
rotation ; and in the selection of stations both con- 
siderations have of course to be taken into account, 
the aim being to make the difference of duration as 
great, and therefore as exactly measurable, as possible. 
The considerations on which the selection of sta- 
tions depends will be dealt with in a simple manner 
farther on. 

^Ve may conveniently call Halley's method the 
^ method of durations ' — a name descriptive of the 
qualities of the method. But it certainly seems a 
mistake to limit the title ' Halley's method ' to the 
case more particularly considered by him.^ AVe may, 
therefore, use both names indifferently. 

Halley's method requires the whole transit to be 
seen, or at least the beginning and end. Apart from 
other difficulties which this requirement introduces, 
the probability of favourable weather both at ingress 
or egress is manifestly less than the probability of 



^ An effort has of late been made to dismiss from use the title 
' Halley's method,' which Sir J. Herschel and others had long used. I 
cannot see why Halley's name should thus be summarily dismissed from 
the position it has so long occupied. 



OF TRAXSITS AXD THEIR COyDITIOXS. 1 01 

favourable Aveather for a single observation only. It 
occurred to Delisle^ when preparations were being 
made for tlie transit of 1761. that assuming Halley 
was right in supposing the moment of contact at 
ingress could be determined Avith great exactness, a 
single observation of the sort might be employed in- 
stead of two terminal observations. 

It is clear that the observer who sees Yenus 
traverse such a chord as I'm' ffig. 13) Avill see the 
transit begin earlier than one who sees her traverse 
such a chord as 1 mAov / is a point more achanced than 
the point T. Suppose noAv that each observer notes 
the exact moment of local time A^dien the transit begins 
(internal contact), and that, knowing his exact longi- 
tude, each can change his local time into Grreenwich 
time ; then these two Greenwich epochs will differ 
by an interval corresponding \o the amount by AA'hich 
/ is in advance of /'. But this gives a geometrical 
relation Avhence the distance between the chords Im 
and /' m can manifestly be determined, just as Avell as 
though the length of each chord were ascertained. 
Hence v v becomes known, and thus, as in the 
direct method, the sun's size and distance can be 
determined. 

Similar remarks apply {mutatis mutandis) to the 
observation of egress. The method, Avhether applied 
at ingress or at egress, is called Delisle's method.^ 

The employment of photography to record the 

^ It is singular that Delisle's name, like Hallev's. is not used in Sir 
G. Airy's programme for the transits of 1874 and 18^2 



102 



TllAXSITS OF VEXUS. 



place of Venus on the sun's face at any particular 
instant need not detain us here, as it manifestly intro- 
duces no new astronomical relations. 

And noAv let us consider how transits of Venus 
recur, in other words, how those opportunities are 
from time to time offered which admit of beino; utilised 
in the various ways above described. 

Let us examine, first, how successive conjunctions 
of Venus are brought about. 

Let the paths of Venus and the earth around the 
sun s (fig. 15) be represented by the circles vv^ and 
E e' ; and let us suppose that Venus and the earth are, 




Eig. 15. — lUutJtrating the conjunctions of the Earth and Yenns. 

in the first instance, in conjunction, as at Y, E, so that 
b YE is a straight line. AVe need take no account, at 



OF TRANSITS AND THEIR COXDITIOXS, 103 

this stage, of the slight eccentricity of the two orbits, 
and of the fact that they are not exactly in the same 
plane. Thus, we may be supposed to b^ looking 
directly down upon the moving planets, which, instead 
of travelling, as they actually do, with a slightly 
varying velocity, are supposed to travel Avith their 
mean or averaoe motion. 

Now, the simplest way of determining when and 
where the two planets will be again in conjunction is 
perhaps the following : — 

Imagine that a straight pointer from the sun to 
Venus, extending to the earth's orbit, like the line 
s V E, is carried round s as a central pivot by the 
motion of the planet Venus. Then whenever this 
pointer comes up to the earth, the three bodies — sun, 
earth, and Venus — are in conjunction. Now, Venus 
travels with a mean motion of 96' 7''*8 per day around 
the sun (completing a revolution in 224*701 days), 
while the earth travels with a mean motion of 59' 8''*3 
(completing a revolution in 365 '257 days^); so that 
in each mean solar day Venus gains, on the average, 
36' 59"'5 upon the earth. This is the rate at which 
our imaginary pointer, starting from a position such as 
S y E, sweeps onwards from the advancing earth, so as 
to again reach the earth by overtaking it, just as the 
minute-hand of a clock, after being in conjunction 
Avith the hour-hand, passes on towards its next con- 
junction, with the excess of its motion over the hour- 

^ Sidereal revoliition is here considered, not the tropical reyolution 
which forms the year of seasons. 



104 TRANSITS OF VENUS " 

hand. We have only, then, to ask how long it will 
take the pointer, with its mean daily gain of 36^ 59^^*5, 
to gain one complete circuit, to have the interval in time 
between successive conjunctions of the earth and Venus 
— ^in other words, there will be just as many days in 
this interval as the number of times that 36^ 59^''5 is 
contained in 360°, or, reducing both to seconds, as 
2219-5 is contained in 1,296,000. The division is 
easily effected, and gives us 583*9 days. 

Our Venus-carried pointer thus takes 583*9 days 
in overtaking the earth. This is more than a year by 
about 218*6 days, in which period, with her mean 
motion of 59' 8'^ '3 per day, the earth travels round 
nearly 21 5|^ degrees. Xow, 216 degrees would be fths 
of a complete circuit. We see, then, that the next 
conjunction-line, S v' E^, must be set almost exactly |-ths 
of the way round from s Y E, or in the position s Yj Ej ; 
the next will have the position s Yg ^2 ; the third will 
have the position s Yg E3 ; the fourth, the position 
S Y^ E^ ; and the fifth will be close up to s Y E, in the 
position SY5E5, about 2\ degrees behind s ye. 

Since the interval between each conjunction is 
about a year and three-fifths, the whole thne occupied 
before the position s v^ e^ is reached by the conjunc- 
tion-line will be five times 1|- years,- or 8 years, less 
the short interval corresponding to the earth's motion 
over the arc E^ E. We see, then, how it comes 
to pass that an interval of eight years brings round 
nearly the same circumstances as at the beginning of 
the interval, and why, therefore, when a transit has 



OF TRANSITS AND THEIR CONDITIONS, 105 

occurred, another may occur eight years later. A 
second interval of eight years, as we shall presently 
see, changes the conditions too largely -(though they 
are still approximated to). 

It may be mentioned in passing that since Venus 
gains one complete circuit on the earth between two 
successive conjunctions, and the earth goes nearly 
eight times round for the five conjunctions just con- 
sidered, it follows that Venus goes nearly thirteen times 
round. In other words, thirteen revolutions of Venus 
are nearly equivalent to eight revolutions of the earth. 

And now let us consider the effect of the inclina- 
tion of the orbit of Venus to that of the earth, still, 
for the sake of simplicity, leaving out of account the 
slight eccentricity of the orbits. 

If EE^, YV^ (fig. 16), represent the two orbits, 
and iE be the place of the earth at the autumnal 
equinox, then the line E e^ represents the intersection 
of the two orbit-planes ; and if, as before, we regard 
the plane of the paper as containing the orbit E e^, then 
the part v v v^ of the path of Venus is to be as re- 
garded slightly above, the part y^ v^ Y as slightly below, 
the plane of the paper. Accordingly, the end of the 
pointer which we have supposed Venus to carry round 
the sun, passes above the semicircle e ^ e^ and below 
the semicircle e^ e^ e. And supposing this pointer to 
be of the length se, so that its end appreciably travels 
round E ^ E^ / (except for the displacement above and 
below the plane of this orbit), it is easy to calculate 
how much above or below the level e eE^ e^ the end of 



I06 T RAX SITS OF VENUS. 

the pointer runs. When in the direction s E or S y! , 
of course the Venus-carried pointer has its extremity 
on the earth's path ; when in direction '^v e or ^v^ e\ 




Pig. 16. — iSliowing the parts {p p' and qq') of the Earth's orbit where 
transits can occur. 

at right angles to E e^ the end of the pointer is at its 
farthest from the plane E e E^ e\ The inclination of 
the orbit of Venus being about S'^ 23-^^, and the dis- 
tance s^ (the earth's distance from the sun) being 
about 91,430,000 miles, it is easily calculated that the 
extremity of the pointer passes above e and below e^ 
at a distance of about 5,409,000 miles. At any other 
point, as p or p^, the end is above or below by an 
amount less than 5,409,000 miles in the same degree 
that p M or p' 31 is less than e S or e s (p 31 p' being 
drawn square to E E^). 



OF TFcAXSITS AXD THEIR COSLITIOyS. 10/ 

^ow. ir is clear that, for a transit to occur, a line 
from the sun's centre through Venus to the earth's 
orbit, at the time of a conjunction^ must not pa>s more 
tlian a certain distance above or below the earth's 
orbit — that is. a conjunction must occur near the 
positions \ E or v' r/. And it is easy to determine 
roughly how near the earth must be to E or e' at the 
time of conjunction, for a transit to occur. For let 
S V E. fig. 17. h'C our imno'innrv pointer at the time of 




Fig. 17. — Illustrating the occurrence of transits. 

a conjunction, and s\ e^ s \' e' lines touching the sun. 
Then it is manifest that if the earth be anywhere on 
the line e y. e ^X the time of conjunction, a line from 
the earth to Venus must meet the globe ^^ s s\ or, in 
other words, there is a transit. But if the earth be 
above e or below e at the moment of conjunction, 
there can be no transit. Xow, s s, the sun's radius, is 
about 426,000 miles, and therefore E e and e' e are 
each less than 426,000 miles in the proportion in 
which V E is less than v s, or, roughly, as 277 to 723 ; 
so that E 6- and E ^' are each equal to about 163,000 
miles — a small distance compared with the actual 
range of the end of our Venus-carried pointer above 
and below the earth's orbit. And it is easilv calcu- 



I08 TRANSITS OF VENUS. 

lated^ that the range on either side of e or y! (fig. 
16)^ within which a transit is possible^ is represented 
by the arcs p^p^ and q^q^ each equal to about 3^ 
degrees. 

ISTow, having found that the circuit of the earth's 
orbit has these two transit-regions^ so to call them, it 
is not difficult to ascertain the general conditions under 
which the conjunction-line will fall from time to time 
upon one or other region. 

Let it first be noted that the points E and E^ are 
at present those traversed by the earth on or about 
December 7 and June 6. The line e s e^ does not^ 
however, bear a fixed position with respect to the 
point M^ but the points E and E^ slowly shift forwards, 
that is, in the direction indicated by tlie arrow. The 
node of Venus's orbit shifts backwards with respect to 
the stellar sphere by about 20^^*5 per annum ; but as 
the point M shifts backwards annually by about 50^^*1 
(the precession of the equinoxes), it follows that the 
nodes Y and Y^, and therefore the points E and E^^ 
advance with respect to M by about 29^^*6 (the excess 
of 50^^'l over 20'^*5) annually. Still, in dealing with 
the general question of the recurrence of transits, we 
must not regard the node of Venus as advancing by 
29^^*6 annually, but as receding by 20^^'5 ; for in what 



^ We require to have 

E/>_ 163,000 
e7~M09700O 

that is, the sine of the arc ^'p= 163 -^5409. Whence e/) is an arc of 
about 1^ 44', and each of the aJrcs j;// and qq' about 3^ 28'. 



OF TRANSITS AXD THEIR COKDITIOXS 109 

has hitherto been said about successive conjunctions 
of Venus and the earth, we have used the sidereal 
periods of both planets, and we cannot substitute the 
tropical year without making corresponding corrections. 

We may regard the system of five conjunction- 
lines shown in fig. i 5 as a spoked wheel, which slowly 
i)ut continuously shifts backwards in such sort that 
any one spoke, S E, shifts to the position s^ E^ in eight 
sidereal years less the time occupied by the earth 
in moving over E-E, or about 2*449 days. This 
shift of position amounts to rather less than 2° 25^ ; 
but as the transit reorions are themselves shiftino; back- 
wards at the rate of 20^^*5 annually, or about 2|' in 
eight years, we have the shift of the. conjunction-lines, 
with reference to the transit regions, equal to about 
2° 22^ in eight years. 

Xow let us suppose that the conjunction-line has 
at starting the position which it actually had on the 
occasion of the transit of the year 1631. Thus, let 
pp^ (fig. 18) represent what may be called the December 
transit region, and q q[ the June transit region^ and let 
S v E, the first conjunction-line, fall so that E is the 
place of the earth on December 6.^ The five next 
conjunction-lines have, as already shown, the positions 
Yj Ej, V2 E2, Y3 E3, Y4 E4, and Y5 Eg ; and we see that E. 
being 2° 22^ from E, while "pp' is an arc of nearly 3|-°, 
Eg falls within j9p^5 and there is again a transit, on or 

^ In the seventeentli century, but corresponding to her position on 
December 9 in the nineteenth century 



no 



TRANSITS OF VENUS. 



about December 4.^ This corresponds to the transit of 
1639. The next five conjunctions take place m due 




Fig. 18. — Iliubtrating the regression of tlie coiijuuctioii-liues over a 
transit region (j>]j'). 

order on the lines marked 6, 7, 8^ 9^ &c. We see, then, 
that there will be no December transits, that is, no 
conjunction within the arc jj p\ until the gradual 
advance of the conjunction-line E.^ Vg has carried it by 
eight yearly steps to the transit region p p\ This 
manifestly requires as many eight-yearly intervals as 
2° 22^ is contained in the arc Ej Eg, or roughly the 
fifth part of the complete circuit ; or, in other words, we 
must multi[)ly 30| by 8 to obtain roughly the number 



In the seventeenth century, or about December 6 in the nineteenth. 



OF TRAXSITS AND THEIR COXDITIOSS. Ill 

of years. This gives 243 as the nearest whole number 
of years ; and this^ it will be noted^ is the interval 
from the December transit of 1631 to the next 
December transit of 1874^ or from the June transit of 
1761 to the next June transit of 2004. But we see 
that while the conjunction-line Eg Vg is travelling by 
eight yearly steps to the transit region p p\ the con- 
junction-line Ej Vj will have travelled by similar ste|)S 
to the position E^ y^, passing over the transit region 
q q , and giving therefore two June transits in the 
middle of the period of 243 years. 

And here^ for the first time we have to note the 
effects of the slight eccentricity of the orbits of the 
earth and Venus. If the two paths were concen- 
tric circles their centre being the sun^ the conjunction- 
lines would be distributed with perfect uniformity, 
so that the arcs E Eg, Eg E^, E^ Ej, Ej Eg, and Eg e. 
would be exactly equal ; but owing to the eccen- 
tricity of the orbits, and the consequent variation 
in the motions of both Venus and the earth, this 
uniformity does not hold. The five arcs just named, 
or others similarly formed from any other conjunction 
as a starting-point, are slightly different in length, 
being largest always when the earth's orbit approaches 
nearest to that of Venus, so that the angular motions 
of the two bodies around the sun differ least, and 
smallest where the orbits are farthest apart so that the 
angular motions of the two bodies differ most.^ 

^ Anything like an exact discussion of tlie varying relative mctions 



The Eai-th 




Venus 


o / // 


c 


/ // 


1 1 10 


1 


37 30 


59 9 


1 


36 8 


57 11 


1 


34 52 



112 TRANSITS OF VEXUS. 

At the present time^ for instance, the conjunction- 
lines have such positions as are indicated in fig. 19, 

of Venus and the earth ^roiild be altogether out of place in a ^-ork of 
this nature. Let it suffice here to note the followinof values : — 



Maximum daily motion . 
jNIean ,. .. 

Minimum ,, ., 

IS^OT^-, the perihelion of Venus is in longitude about \2^\°, the perihelion 
of the eartli in longitude about 99 J°, or nearly 25° behind. As the eccen- 
tricity of the earth's orbit is greatest, being nearly twice that of Venus's 
orbit (if measured in miles, still greater),, we should not be far wi^ong 
in taking the earth's perihelion for the point of nearest approach to the 
orbit of Venus ; but inasmuch as opposite this point Venus is approaching 
perihelion, we somewhat diminish the longitude to obtain the actual 
point of nearest approach, which will be in about 70° of longitude, or at 
the place occupied by the earth on or about December 2. Here the 
daily motion of the earth is about 1° 0' 56'^ that of Venus about 
1° 36' 49", the excess of the motion of Venus in longitude being there- 
fore 35' 44'^ "[When the earth is in longitude 90° her mean daily motion 
is about 1° 1' 7 '5'', that of Venus in the same longitude being about 
1° 37^ 0"5", an excess of 35' 53"; so that the daily motions are not so 
nearly equal as in longitude 70°. In fact, it chances that the motions 
of Venus and the earth in conjunction are nearest to equality almost at 
the time corresponding to a December transit.] Now, at the opposite 
part of the two orbits, or in longitude about 250°, we have the earth's 
daily motion about 57' 29'', that of Venus 1° 35' 19", an excess of about 
37' 50", or more by about 2' 6" than that in longitude 70°. It follows 
necessarily that successive conjunction-lines (after successive eight- 
yearly periods) fall nearer together in the June part of the orbits than 
in the December part. For the exact eight years which carry the earth 
from position e (fig. 15), to position e again soon after conjunction at Ej 
with Venus at Vg, correspond to thirteen complete revolutions of Venus 
plus 0*955 days, wherever e may be. Now letv be the place reached by 
Venus when the earth is at e, then v v is the space traversed by Venus in 
0'955 days. But v v also measures the gain of Venus on the earth, while 
the earth has been passing from e. to e. Now, in longitude 70°. Venus, 
being nearer her perihelion, moves faster than in longitude 250° ; hence 
on this account the arc v v will be greater for a December conjunction, 
than for a June one. Since, then, the gain v v of Venus is greater at a 



OF TRANSITS AND THEIR CONDITIONS, 1 13 

where the eccentricities of the two orbits are properly 
shown, and the conjunction-lines are placed in longitude 

December conjunction than at a June one, while yet it accrues at a less 
rate as we have seen above, it follows that it requires a longer time to 
accrue : in other words, the arc corresponding to e^ e requires a longer 
time, and if the earth moved imiformly would be a longer arc at a 
December conjunction than at a June one. But the earth is moving 
faster in December than in June ; a fortiori therefore the arc corre- 
sponding to EE5 will be greater for a December than for a June conjunc- 
tion. Thus is explained the greater distance between the transit lines 
of a December pair than between the corresponding lines of a June pair. 
See Plate I. To further illustrate this, and also to make this reasoning 
more directly applicable to the subject matter of this chapter, I will 
now proceed to calculate the actual displacement of the conjunctiourline 
in eight years, for the two transit regions respectively. 

Suppose a conjunction to occur on or about \ ^ ^ >, Then 

in eight sidereal years from this conjunction the earth has gone eight 
times round, while Venus has gone round thirteen times j^lus her motion 
in 0'95o d. This motion takes place at the daily rate of < ,0 o-/ i o// !> 

and therefore places Venus in advance of the earth by < -. -^// ^ ; 

and the daily gain of Venus, or < no«q// ( is contained < rj.j^r.- \ 

times in< r ,^/.// >. Therefore conjunction must have occurred 

I 9-40' 7 r eS'^lie^j 0^ since the earth's daily motion is < 04.4.1.// \ 

conjunction must have occurred ^ 00 -i 0/ -i/f f in longitude behind the 
conjunction-line of the earlier transit. Diminishing each arc by 2J' for 

the change of the nodal line in eight years, we obtain a motion (with 

{2© 350 
^o-f-/ [>j near enough for our present 

purpose. 

In the above, no account is taken of perturbations of the motions of 
Venus and the earth by the other planets. 

It will be convenient to add here a more exact calculation of the 
transit arcs_p_p' and qq', fig. 16. "We may follow the same plan as at 
page i07. 

I 



114 TRANSITS OF VENUS, 

3% 77% 155% 225% and 292% which correspond, nearly 
enough for our purpose, to the inferior conjunctions of 



. /Go 

^^ l66 



We have, — the distance of Venus from sun at < n l r ^^^® 

^\ci±(\(\Ci \^^^^ (where the earth's mean distance is taken as 
91,430,000 miles), and the earth's distance in the same longitudes respec- 
tively is < no'o-iy'AAA \ miles; so that the distance of the earth from 
Venus at conjunction is respectively < o/^^oo aa/v > miles; and diminish- 
ing the sun's radius (which here for greater exactitude we take at 426,450, 
its true value if sun's mean distance be 91,430,000 miles) in the ratio 

r 24,171,000: 65.865,000 1 i ,. • ^ ^i r ^ ^^ 

{26,423;000:66,394;000l'^' obtain for the distance corresponding 

to Ee and Ee' fig. 17 the value < ign'^oQ \ miles; audit thence follows 

^:»E = E/=156,500cosec(3° 23^0 = 2,645,300 miles 
^■^^^^ ^e' = e' $' = 169,720 cosec (3° 23i-') = 2,868,700 miles 

while the arc-measure of _p e, or -^, is equal to 1*^ 41', so that pp' is an 

arc of 3° 22' ; 

ce' 
and the arc-measure of o'e', or^, is equal to 1° 46', so that qgf is an 

E S 

arc of 3° 32'. 

These values are for the centres of Venus and the earth. It would 
be easy, but is scarcely worth while, to calculate them for exterior or 
interior contact, and for the whole earth, — that is, to determine the arc 
■pp^ or q q' for the extreme cases where if any part of Venus be seen on 
the sun's disc from any part of the earth, a transit shall be considered to 
have taken place, or where no transit shall be considered to have taken 
place unless the whole of Venus be seen within the sun's disc even from 
the station which throws her farthest from the sun's centre at the moment 
of nearest approach. Into such niceties, however, we need not here 
enter, as they are merely questions of curiosity, and neither present any 
difficulty nor involve any important principle. 

It will be seen that since at two successive conjunctions near 
December 7, the conjunction-lines are separated by 2° 37' 26" (or about 
2^ 35' measuring from the node), while the transit arc is about 3*^ 22' in 
range, whereas at two successive conjunctions near June o, the conjunc- 
tion-lines are separated by only 2° 18' 1'' (or about 2^ 15' measuring 



OF TRAXSITS AXD THEIR CONDITIO SS. I13 

Venus on the elates^ September 26^ 1871^ December 9. 
1874, February 24, 1870, May 5, 1873, and July 14, 
1876. Xow it is clear that the conjunction-line y- e. is 




i'ig. 19. — ibJiowing me actual position 01 conjuiLction-iiiie.i> of tnu earth 
and Yeniis. 

farther from the nodal line v^ e' than is the conjunction- 
line Y3 E3. In fact the longitude of y\ the node, is 
about 255^° ; and V3 is only SO^"" or so from the node, 
while v^ is about 36%° from the node. Hence the con- 
junction-line Y- E. will take longer, in marching up by 
eight yearly steps to y^, than the half of the period of 243 
years, which is the time in which it comes up to the 

from the node), and the transit arc has a range of 3° 32'. there is a much 
greater chance of a pair of transits when the conjunction-line is sweeping 
over the June transit-region, than when it is sweeping over the December 
transit-region. 

I 2 



Il6 TBAXSITS OF VEXUS. 

position Y3 E3. We need not enter here into the calcula- 
tions by which the exact time occupied in each part of 
the progression is determined. Let it suffice that the 
considerations just adduced serve to explain how it is 
that from June 1761 the epoch of the first transit 
of the last pair, to December 1874 the epoch of the 
first transit of the coming pair, is a period of only 
113^ years, whereas from December 1874 to June 
2004 the epoch of the first transit of the next pair, 
is a period of 129| years. The former is the time 
occupied by the conjunction-line in moving from the 
node v^ to the position Vg, when of course the other 
conjunction-lines have the position shown in fig. 19, 
and December transits occur ; while the latter is the 
longer time occupied by the conjunction-line V- E^ 
in moving up to v^ E^ The sum of the two periods 
113^ and 129-|- is the period 243, just mentioned as 
that which separates two first transits either of a June 
pair or of a December pair. It is clear that if we 
start from the first of a June pair, we have the following 
intervals between successive transits: 8 years, 105|- 
years (8 from 113-|- years), 8 years, 121^ years (8 from 
129^ years), and so on continually in the order 8, lOoi, 
8, 113^, so long as there is no break on account of a 
single transit occurring instead of a pair. This can 
manifestly happen, both at the December region and at 
the June region, though more readily at the former 
than at the latter. The conjunction-line steps back (so 
to speak) over the December region by steps of about 
2"" 35' (see note, p. 113), and this region is about 3° 22' 



OF TEAS SITS ASD THEIR COXDITIOXS. II7 

in width ; so that if the first step falls on the beginning 
of the interval or within 45^ of it^ the next will fall 
within the transit region^ and there will be two transits ; 
but if the first falls anywhere between 45' and 2° 35' of 
the beginning of the transit region the next vdW fall 
outside. The number of occurrences of a pair of transits 
in the December region will therefore bear to the 
number of occurrences of but one transit^ the propor- 
tion which 45' bears to 1° 50'^ or which 9 bears to 22. 
That is^ on the average of a great number^ there will 
oftener be one transit only in the December region 
than a pair. Applying the same reasoning to the 
June period, we have (see note, p. 113) 2° 15' for the 
reo^ression and 3° 32' for the width of the transit-reo:ion, 
giving 77' favourable for the occurrence of a pair ot 
transits, and 58' for the occurrence of but one. Hence, 
on the averao^e of a oTeat number of cases of June 
transits there will be a pair oftener than a single 
transit, in about the proportion of 77 to 08, or nearly 
as 4 to 3. 

It chances, however, that the interval between one 
December set and the next, or between one June set 
and the next, so nearly reproduces the same exact 
circumstances, that when a pair of transits has occurred 
jU one instance it is almost certain that on the next 
occasion there will be a pair also. Accordingly, for 
many successive passages of the December transit- 
region, and for a yet greater number of successive 
passages of the June transit-region, there will be a pair 
of transits at each passage. Then will foUoAv long 



Il8 TRAXSITS OF VEXUS. 

intervals during which each passage will bring but a 
single transit. The series 8, 105^^ 8, 121^,8, &c. will 
then be modified into the series 113^, 129-^, 113-^, &c. 
But various other modifications occur in the course of 
long periods of time. Thus the triplet of intervals 
105^5 8, 121|-^ in the complete series may be changed 
either into the pair 113^, l^H? ^^ ^^^o the pair 105^, 
129^ ; while the triplet 121 J, 8, lOS^, may be changed 
either into the pair 129^, 105^, or into 121^, 113^, 
according to circumstances. 

So much for the order in which transits recur, 
either at the ascending node in December or at the 
descending node in June. Let us now consider how 
stations are selected for applying the various methods 
which are available. 

Let s, fig. 20, represent the sun, and v Venus, 
the arrows showino; the direction in which Venus 




Fig. 20. — Illustrating Yenus's shadow-cone. 

and the earth are travelling around s. Let svp 
represent the Venus-carried pointer of which we have 
already made frequent use, its extremity p being in 
the figure rather above the earth's orbit, and travelling 
onwards with the excess of Venus's motion, so as to 
overtake the earth. Xowlet a cone, havino; the centre 



PLATE X, 




Fig. 22, Ingress 1631 and 1874. Fig. 23, Egress 1G31 and 1874. 




Fig. 25, Ingress 1639 and 1882. Fig. 26, Egress 1H39 and 1882. 

Illustrating Passaoe of Yenus's Shadow-coxe over Earth in 

1631, 1639, 1874, AND 1882. 



OF TRANSITS AXD THEIR COXDITIOXS. II9 

of Venus, Y, for its vertex, and s v for its axis, be 
supposed to envelope the sun after the manner shown 
by the section s v s' in the figure, and let the prolonga- 
tion of this cone beyond v, be v \ v ^ v v being a 
circular section through /;. Then we may regard this 
circular section (which corresponds to e e^ in fig. 17) 
as travelling onwards like a gigantic wheel more than 
300,000 miles in diameter, to overtake E ; and if v is 
near enough to a node, then will this great circle pass 
athwart E in such sort that E will traverse a chord of 
the circle v v\ Let us try to picture such a passage. 
Suppose V to be near an ascending node so that the 
circle v v^ as it overtakes E has a slight upward motion : 
also if we are looking from s towards E (and v v^ were 
a real circul"ar outline) we should see v v' moving from 
right to left to overtake E. It will be convenient to 
regard e as at rest so that we consider only the excess 
of the motion of ?; v over that of the advancing 
earth. 

In fig. 21, Plate X., v l v represent the circle v v 
offio;. 20 on an enlaro^ed scale at the moment when 
the earth e e^ is first touched at the point z. At this 
moment an observer at i will of course see the centre 
of Venus just crossing the edge of the sun. (This is 
manifest from fig. 20, where we see that a line drawn 
to V from any point, as z, fig. 21, on-the surface of the 
cone V Y V will touch the globe s s ,') To an observer 
at i then, but to no one else on the earth e e\ transit 
will have begun (reference being always made to the 
centre of Venus). 



120 TRANSITS OF VEXVS. 

The centre of v v' advancing from Pj to Pg^ the 
circular section reaches the position v i^ v' touching the 
earth at i . Its edge has all this time been passing 
over the face of the earth ee\ moving nearly parallel 
to itself ; and transit has now begun for every part of 
the illuminated hemisphere of the earth. So that i' is 
the place on the earth where transit begins latest. AVe 
have then i the place of earliest beginning (or^ as it is 
technically called^ tlie pole of accelerated ingress), and i' 
the place of latest beginning (or the pole of retarded 
ingress). The points i and i' are not exactly opposite 
each other even on the circle e e\^ still less are they 
exactly opposite points on the glohe e e , which has 
been rotating all the time that the centre of v v has 
occupied in advancing from Pj to P^^, a process lasting 
several minutes (more than 25 m. for instance in the 
transit of 1874^ and 17 m. in the transit of 1882). 

Stilly as a first approximation^ we may consider the 
points i and ^^ to be at opposite extremities of a 
diameter of the earthy taking (in order to reduce errors 
as much as possible)^ the face of the earth turned sun- 
wards when the advancing edge of v v^ crosses the 
centre of the earth's disc^ and taking that diameter i { 
of the earth which is at right angles to the advancing 
edge in this intermediate position. AYith this assump- 
tion^ the passage of the edge of the circle v v over the 

^ For a tangent to viv' at i is not parallel to a tangent to -y i' v' at i, 
"vrliereas tangents at the extremity of any diameter of a circle are neces- 
sarily parallel. (In fig. 22, the tangents at i and i', are taken parallel to 
a tangent to the circle v v' at the point where, and at the time when, its 
edge crosses the centre of the disc i i' of fig. 21.) 



OF TRANSITS AXD THEIR COXDITIOSS- 121 

earth's face is illustrated by fig. 22 (Plate X.) which 
represents ou an enlarged scale the disc z/ of fig. 21, 
the edge of the circular shadow being represented in 
ten successive stages of its (supposed) uniform advance. 
The earth is shown in the proper position for a 
December transit. Kothing can be easier than to 
determine the position of i and i ^ the poles of ac- 
celerated and retarded ino^ress. For all the circum- 
stances of the motion of Yenus are known, whence the 
motion of the projection of her centre along p^ p., Pg P4 
is detemiined. AYith reference to the earth e e we 
know also what face of the earth is turned sunwards 
at the moment when the section v v^ crosses the centre 
of the earth's disc. The size of the section v v is also 
known (see note at p. 1 14 where it is calculated both for 
December and June transits), except of course in so far 
as it depends on the more exact determination of the 
sun's distance. And indeed, we see from this in a 
new way, hoAv the circumstances of the transit as 
viewed at different stations depend on the distance of 
the sun, and therefore conversely how our estimate 
of the sun's distance depends on the circumstances of 
the transit as viewed at different stations. For while 
the disc e e' of the earth has a known diameter of 
about 7,900 miles, and the section v v' has the posi- 
tion and path of its centre along p^ p^ determinable 
independently of the sun's distance, the size of the 
section (as we see from the note, p. 114) depends on 
the sun's distance and size. Xow if we enlaro-e or 
diminish v v\ while leaving e e unchanged in position. 



122 TRANSITS OF VENUS. 

and the motion of the centre of v v along p^ p^ also 
unchanged^ we manifestly modify the nature of the 
passage of the edge of v v^ over the disc e e\ 

The section v v^ passing on, arrives at length at the 
position Y e v^ touching the disc of the earth at e. At 
this moment the centre of Venus is seen, by the observer 
at e^ on the edge of the sun ; in other words, egress 
(of the centre of Venus) is taking place, and e is the 
station where egress is first seen. The section v v^ 
passes on until it has the position Y e^ \\ when it is 
about to leave the earth finally, its last contact with 
the earth being at / — where egress takes place latest. 
In the interval the edge of Y Y^ has been passing over 
the disc e e\ moving nearly parallel to itself: we 
have then e the pole of accelerated egress and e the 
pole of retarded egress. As in the case of ingress, e 
is not exactly opposite to / even on the circle e e\ 
while rotation has affected the globe e e\ so that e is 
still farther from being opposite to / on the earth. 

AYe may, however, in this as in the former case, 
regard (for a first approximation) e and / as points on | 
opposite extremities of a diameter of the earth, taking 
the moment intermediate between earliest and latest 
egress. With this assumption, the passage of the edge 
of the circle Y Y^ across the earth's face is illustrated 
by fig. 25 (Plate X.), which represents the disc e e' of 
fig. 21 on an enlarged scale, the edge of the circular 
shadow beino; shown in ten successive stao;es of its 
supposed uniform retreat. The earth is shown in the 
proper position for a December transit. 



OF TRANSITS AXD THEIR COSBITIOXS. 1 23 

It need hardly be said that the face of the earth 
turned sunwards when the section v v^ has advanced 
to the position Y v^ is greatly changed from the face 
which had been turned sunwards when ingress was in 
progress. But the time of egress is easily calculable^ 
like that of ino:ress, from the known motions of Venus 
iivA the earth ; the face of the earth turned sunwards is 
also known ; and all the circumstances of the passage 
of the edo:e of y y^ over the earth's face at egress are 
easily determined. In fact, all that was said respecting 
ingress is true, mutatis mutandis, in the case of egress. 

The conditions represented in fig. 21 are actually 
those of the transit of 1874. The shadow cone of 
Venus passes slantingly upwards wdth reference to 
the earth, and the centre of the circular section v v 
passes north of the earth. The earth passes, therefore, 
through the shadow section as along the dotted line, 
in the manner shown farther on in fig. 35. But the 
conditions of the transit of 1631 so nearly resembled 
those of the coming transit that fig. 21 conveniently 
illustrates both transits. 

In order to more thoroughly master the above 
reasoning, the reader w^ould do well to run over it 
again, using figs. 24, 25, and 26, instead of figs. 21, 
22, and 23 respectively. Fig. 24, with its companion 
projections, illustrates the transit of 1882 (and approx- 
imately also the transit of 1639). See also fig. 35. 

Then the reader can apply the explanation given 
above, with very slight changes, to the case of June 
transits, illustrated by fig. 27. Figs. 28 and 29 are 



124 



TRANSITS OF VEXUS. 



the companion June projections of the earth for the 
earlier of a pair of June transits (as the transits of 
1761 and 2004), while figs, 30 and 31 are the com- 




Yisi, 27.— Illustrating the passage of Veuuss shadow-cone over the earth 

dtiring the transits of 1761, 1769, 2004, and 2012. 
rig. 28.— Ingress, 1761 and 2004. Tig. 29.— Egress, 1761 and 2004. 
Fig. 30.— Ingress, 1769 and 2012. Tig. 31.— Egress,' 1769 and 2012. 

panion projections for the later of a pair of June 
transits (as the transits of 1769 and 2012). Moreover 
it chances, so nearly similar in position are the northern 
and southern transit chords for the four transits just 



PLATE XL 




TKANSITS OF 1874 AND 1882. 



ILUJSTRATIXG internal contacts and MID-TRANSn, AND SHOWING RELATIVE 
DIMENSIONS OF THE DISCS OF VeNUS AND THE SUN. 




1TN<5 IXTEBNAL CONTACTS AND MID-TRAXSTT, AND SHOTTINO RELATITE 

btMENsroy^: ok the dt^cs of Vvvrs asd Tt^l-- Srv. 



OF TRANSITS AND THEIR CONDITIONS- 1 25 

named, that one and the same figure illustrates all four 
with sufficient approximation for illustrative purposes. 
Now it is easy to see how Delislean stations are to 
be selected in any given case. Take the transit of 
1874. We find first the hours at which the circle v 0^ 
(fig. 21) crosses the centre of the disc of the earth 
i e i e' at the beginning and end of the transit, or, 
which is precisely the same thing, the moment when 
the centre of Venus, as seen from the earth's centre, 
reaches the positions h and h\ Plate XI. This is in 
point of fact the ^ calculation of the transit,' and de- 
pends on principles corresponding to those* involved in 
the calculation of an eclipse. Having these two 
epochs of the beginning and end of transit, and also 
the positions of the transit chord h V Plate XI., and 
ah of fig. 21 Plate X., we make a sun- view of the 
earth at the beginning of the transit as Plate XII., 
and another of the earth at the end of the transit as 
Plate XIII. (Plates XII. and XIII. really represent 
the aspect of the earth for the times of internal con- 
tact — illustrated in Plate XI. — at the beginning and 
end of transit, but they sufficiently illustrate the present 
description). 

Then the positions of the points i and i! fig. 21, 
Plate X. are known at once, from the geometrical 
relations pictured in fig. 21,^ and thus we have the 
poles of accelerated and retarded ingress placed as i 
and a in fig. 22, Plate X., or as A and B in Plate 

^ Of course tlie vertical line x s in figs. 21, 24, and 27, represents 
north and soutli line of the earth's disc lei' e'. 



126 TRANSITS OF VEXUS, 

XII. 3 these positions being the same, it will be observed, 
as the positions of i and i^ on the small disc i e i e 
of fio;. 21. The observers of the accelerated ino-ress 
must be near i on the illuminated hemisphere ii\ fig. 
22, while the observers of retarded ingress must be 
near i. The amount of acceleration or retardation 
will depend on the distance from cc, a station at any 
point in any one of the parallels in fig. 22 having 
equal acceleration or retardation (according as the 
parallel is nearer i or /). The parallel lines of the 
figure are of course circles on the globe of the earth ; 
and i and i are the poles of these circles.^ 

Again, the positions of the points e and e\ fig. 21, 
Plate X., are known ; and thus we have the poles of 
accelerated and retarded egress placed as e and / in 
fig. 23, Plate X., or as c and D in Plate XIIL, these 
positions being the same as those of e and e in the 
small disc iei e of fig. 21. The observers of the 
accelerated egress must be placed near e on the illu- 
minated hemisphere e e' fig. 23, while the observers 
of retarded egress must be placed near /. The amount 
of acceleration or retardation will depend on the dis- 
tance from c c\ a station at any point on any one of 
the parallels of fig. 23 having equal acceleration or 
retardation (according as the parallel is nearer e or e ), 

1 The acceleration or retardation at a station for observing ingress 
manifestly varies as the distance of the station from the plane of the 
great circle having i and i' as poles ; and similarly for retarded ingress, 
and for accelerated and retarded egress. Or in other words, the accele- 
ration or retardation varies as the cosine of the arc-distances from i or i'. 



I LATE XII. 




SUX-VIEW OF THE EARTH AT THE BEGIXXIN'G OF THE TRAXSIT OF 1874. 



1. Station at Hawaii. 

2. ., ,, Kergiielen Island. 
8. „ ,, Rodriguez, 

4. ,, ,, Xew Zealand. 

6. ,, ., Nertsehinsk. 

7. ,, (proposed only) at Possession Island. 

8. ,, ,, Mauritius. 

9. ,, in North. China. 



PLATE XI I L 




Sun- VIEW OF THE Earth at the E>'d of the TEA^■SIT of Ih'i. 



2. Station at Kergnelen Land. 

3. ., „ Piodrignez. 

4. „ in XeAv Zealand. 

5. ., at Alexandria. 

6. ., „ Nertschinsk. 

7. ,, (proposed only) at Possession Island. 
,S. ., ., Mauritius. 

'&. ,. in North China. 

10. The North Indian Ptegion (now occupied). 



PLATE XI W 




SUN*-VIF.W OF THE EaUTH AT THE BKGIXN'IN'G OF THE TRANSIT OF 1S82. 



1. Sir G. Airr's proposed station at Ptopiil-e Bav. 

2. ., ,. on Possession Inland. 




U.^e Bav. 



PLATE XV. 




Srx-VIEW OF I'HE EAItlH AT TflK EXD OV THK TraX.-IT OF Ij-'J. 



1. Sir Cf. Airy's proposed ^ta:^on nt Repnise Ea^. 

-• v •, Ou Pussession Istand. 



OF TRANSITS AND THEIR CONDITIONS 12 J 

These parallel lines of the figure are circles on the 
globe of the earth, and e and e^ are the poles of these 
circles. 

Similar remarks apply to the case of the transit of 
1882, illustrated by figs. 24, 25, and 26, Plate X., and 
by Plates XIV. and XV. The reader is recom- 
mended to go over the last three paragraphs afresh, 
using these last-named figures and j)lates. 

It is easily seen that Delisle's method is applicable 
in every possible case. The poles of accelerated and 
retarded ingress and egress lie always (as 2, i\ e, and /) 
at the edge of the illuminated hemisphere, and stations 
can always be found near to these points, and in sun- 
light. Xor do the conditions of success depend at all 
upon the position of the chord of transit. We see 
indeed that in the case of a short chord as in fig. 21, 
the difference of time between ingress at i and i\ or 
egress at e and e\ is greater than in the case of^a longer 
chord as in fig. 24 ; for Pj Pg and Pg p^ are greater in 
fig. 21 than in fig. 24. But it is easily seen that this 
advantage in the case of the shorter chord is counter- 
balanced by the slowness with which Venus crosses 
the sun's edge.^ Of course the more slowly Venus seems 
to cross the sun's edge the more diflScult it is to deter- 
mine the true moment of contact whether at ino-ress or 
egress, complicated as contact is by the phenomena of 
black-drop formation. 

^ Plate XI. shows us that from b to the centre of Yenus's disc at ? is 
greater than from s to the centre of her disc at i'. In fact this slowness 
of crossing corresponds exactly to the lengthening of the distances Pj p., 
and P3 P4. 



128 TRANSITS OF VEX US. 

Delisle's method is then always applicable, and 
always under similar conditions. It is otherwise with 
Halley's method. Let us briefly consider this method 
in the approximate manner already used for Delisle's 
method. 

To apply Halley's method both the beginning and 
end of transit must be seen. Now ii\ fior. 22, &c., 
enlarged into a sun-view of the earth as in Plate XII. 
(for the case of the transit of 1874), shows the face of 
the earth in sunlight when transit begins, while e e\ 
fig. 23, similarly enlarged, shows the face of the earth 
in sunlight when transit ends. AYe must select stations 
common to both these projections or sun-views of the 
earth in the case of any transit we are dealing with. 
For example, in the case of the transit of 1874, we see 
that such a station as 1, near A in Plate XII. (one of 
the Sandwich Islands), though excellent for observing 
the beginning of the transit by Delisle's method, cannot 
be employed for Halley's, because this station has 
already passed to the dark side (in other words, the sun 
has set there) before the end of the transit when the 
face of the earth pictured in Plate XIII. is turned sun- 
wards. Ao;ain, the station marked 5 in Plate XIII. 
(Alexandria) is an excellent station for seeing the end 
of the transit by Delisle's method, but it cannot be em- 
ployed for Halley's, because it is on the dark side of 
the earth (in other words, the sun has not risen), at the 
beo-innino; of the transit, when the face of the earth 
pictured in Plate XII. is turned sunwards. But at 
any station in Australia, for example, the whole ti^ansit 



OF THAXSITS AXD THEIR COyDITIOSS. 1 29 

can be seen, and therefore Halley's method could be 
employed there so far as visibility of transit is con- 
cerned. It remains, howeyer, to select among stations 
where both the beginnhig and end can be seen, those 
particular stations where the transit is considerably 
lengthened and shortened in duration compared with 
the mean transit (transit of Venus's centre supposed 
to be seen from the earth's centre). In the case of 
Delisle's method, whether applied to ingress or to egress, 
we had two poles (z and i^ for ingress, e and / for 
e2:ress), and could estimate the value of any station 
at once by referring its position to these poles. AVe 
have now to inquire whether there are any correspond- 
ing Halleyan poles — a pole of lengthened duration, and 
another pole of shortened duration. I believe Encke 
was the first to point out that there are such poles and 
to give an analytical proof of the fact ; but the follow- 
ing simple geometrical demonstration is, so far as I 
know, original,^ 

The parallel lines across the disc of the earth in 
fig, 22, represent circles on the earth having /, 1! as 



^ Prof. Adams mentioned the fact that there are such poles, and 
indicated their position, at a meeting of the Astronomical Society at 
which I was present — March 1873, if I remember rightly. I submitted 
to him a day or two after the demonstration given in the text, and in his 
reply he remarked that the demonstration was the geometrical equiva- 
lent of the reasoning by which he had been led to recognise the existence 
and position of the Halleyan poles, as well as the law according to 
which the lengthening or shortening of the duration varies with distance 
from the poles. Subsequently I learned from 31. Dubois' work, already 
ofcen referred to here, that Encke had anticipated Adams in recognising 
"hese relations. 



130 TRANSITS OF VENUS. 

poles, and corresponding to times of ingress successively 
later and later, by equal intervals, as the parallel is 
farther -and farther from i. Now if we suppose the 
o'lobe of the earth rotated about an axis ii\ these 
parallel circles will still appear as parallel and equi- 
distant straight lines. In fact, so long as the points 
i and i^ are on the edge of the visible disc the parallel 
circles will appear as equidistant parallel lines. Similar 
remarks apply to the parallels in fig. 23'; so long as e 
and / are on the edge of the visible disc these parallel 
circles will appear as parallel and equidistant lines. Let 
us suppose, then, that the globe of the earth is so placed 
Avith respect to the observer that all four points /, i , 
<^, and e^ are on the circumference of the visible disc. 
This is clearly possible, for i i are extremities of one 
diameter, ee those of another diameter of the sphere, 
and any two diameters must lie in one plane, which 
plane intersects the sphere in a great circle ; so that we 
have only to place the sphere so that this great circle 
sha.ll form its apparent outline, to have i, i\ e^ and e 
(the extremities of two diameters of this great circle) 
on the outline of the visible disc. 

Now let fig. 32 represent on an enlarged scale the 
face of the globe thus brought into view, i^ and ij. 
corresponding to the points i and 2^, while E^ and E 
correspond to the points e and e\ Also the number 
of parallels has been doubled to make the illustration 
more complete, the maximum acceleration and retard- 
ation at ingress and egress being divided into ten 
equal parts corresponding to the ten equal spaces on 



OF TRAXSITS AND THEIR COXDITIOXS, 131 

either side of the lines e e and c c\ For convenience 
of explanation this maximum is regarded as 10 minutes, 
which is a little short of its value in the transit of 1874 
and a little in excess of its value in the transit of 1882. 
Xow consider any point a where a parallel of one 
system-crosses a parallel of the other system. Since 
a lies on the fourth parallel from c c^ towards i^, the 




Fig. 32. — Illustrating the position of the Hall cyan poles between the 
Delislean poles. 

ingress is accelerated by 4 minutes, and since a lies on 
the third parallel from cc towards E,., the egress is 
retarded by 3 minutes. On the whole, therefore, the 
duration of the transit at a is 7 minutes greater than 
the mean. At the point b where the next parallel 
from la and the next toicards E^ intersect, ingress is 

K 2 



132 TRANSITS OF VEXVS. 

accelerated 3 minutes^and egress is retarded 4 minutes ; 
so that the duration here, as at «, is 7 minutes greater 
than the mean. At the point m the ingress is accele- 
rated 5 minutes^ and egress retarded 2 minutes ; so that 
at m also duration is lengthened 7 minutes. The same 
is the case at n. These points in^ a^ b, and n, lie mani- 
festly on a straight line Avhich produced either way 
to k and V passes through other points of intersection 
of our two systems of parallels, at which points, by the 
method of reasoning already applied to «, b^ m, and n, 
the duration is lengthened by the same number of 
minutes. At e, the lengthening is similarly shown to 
be 8 minutes, and the same at all points on the line 
/ e l\ At rf, the lengthening amounts to 6 minutes, and 
the same at all points on the line j ef. Along c o c' 
the duration has its mean value. And at any point 
on jj^, k k^, or IT, on the other side of C o C, the 
transit is shortened by six, seven, or eight minutes, 
resj)ectively. So with other cases for all points over 
the disc c o c', 

Xow very little knowledge of geometry is required 
to show that tliese lines jj\ kk\ ll\ jj^ k k^, and 
1 r, and the other lines of fig. 32 similarly obtained, 
form a series of parallel equidistant lines ; these lines 
being parallel to c O c', the bisector of the angles 
Ej. o ij. and ij, o e^,. These parallel lines are parallel 
circles on the sphere, having for poles the two points Hi 
and Hg the middle points of the arcs i E^. and i^. e^. 
The farther one of the dotted parallels is from c o c' 
towards Hi the greater is the lengthening of the transit, 



OF TRAXSITS AXD THEIR COXDITIOyS. 1 33 

and the farther such a parallel is from COO towards 
H, the greater is the shortening of the transit. The 
absolute maximum duration is at H^^ and the absolute 
minimum is at H,. These points, then, are the Halleyan 
poles^ and any one of the parallel circles having these 
points as poles 'indicates the position of stations at 
which the lengthening or shortening is in proportion 
to the distance of the plane of the circle from the plane 
of the great circle o 0^ towards H^ or Hg respectively. 
But while the Halleyan poles and circles corre- 
spond thus geometrically with the Delislean poles and 
circles^ there is one important difference. A Delislean 
pole for any phase is a point where the sun can actually 
be seen at that phase. But this is not necessarily the 
case with a Halleyan pole. The northern Halleyan 
pole for example, in the transit of 187-i, is. by what 
has just been shown, the point midway between the 
A of Plate XII. and the d of Plate XIII. d being 
still on the darkened side of the earth at the time 
pictured in Plate XIL, and a having passed to tlie 
darkened side at the time pictured in Plate XIII., it 
is manifest that the middle point of an arc from D tc 
A must also lie on the darkened side at both these 
epochs ; and therefore the northern Halleyan pole, 
though geometrically the point where transit lasts 
longest, is in reality a point where neither the begin- 
ning nor the end of transit can be seen. On the other 
hand, the southern Halleyan pole in 1874, is in sun- 
light throughout the whole transit, as we see by noting 
that the points B and c of Plates XII. and XIII. are 



134 TRANSITS OF VENUS. 

themselves in sunlight throughout the transit^ and that 
therefore the point midway between them must be 
so. The relations here described are those illustrated 
in fig. 32, where the dark lune i^ c ij. represents a 
])art of the eaith where the beginning of the transit 
is not seen, the dark lune e,. c e^ representing a 
part Avhere the end is not seen, and rii lying on 
a part where these lunes overlap, on which therefore 
neither the beo-innino^ nor end of the transit can be 
seen. 

The reader will find no diflficulty in making a 
corresponding construction to illustrate the transit of 
1882. In fact, so far as the parallels are concerned, 
fig. 32 will represent the case of the transit of 1882 
very nearly, for we see from Plates VL and VII. that 
the distance between the two northern Delislean poles, 
and therefore between the two southern, is nearly the 
same in both transits — in other Avords, the arcs corre- 
sponding to i^ E,., Ea If in fig. 32 are nearly right for the 
transit of 1882. But the darkened lunes must have 
the position they assume when fig. 32 is inverted ; for 
we see from Plates XIV. and XV. that while the 
northern Halleyan pole is in sunlight in 1882, the 
southern is on the darkened hemisphere. 

But besides that one Halleyan pole or the other is 
so placed that no part of the transit can be seen from 
it, the circumstances of diflFerent transits vary as re- 
spects the advantages offered by Halley's method. 

For example, take Hg the accessible Halleyan pole 
in such a transit as that of 1874. We see that at this 



OF TRANSITS AXD THEIR COXDITIOXS. 1 35 

point the ingress is retarded and egress accelerated by 
the maximum acceleration or retardation, less only 
about If tenths, so that the shortening is less than the 
sum of the maximum acceleration and retardation by 
only 3|- tenths of either. But if E^^ and i^ were farther 
apart the shortening of the transit would not be so 
o-reat. This is seen from fig. 33, which illustrates the 



Hi-. 




Fig. 33. — Illustrating a case unfavourable for Halley's method. 

conditions of the transits of 1761 and 2004. Here e^ 
and If are farther apart than i.^ and E, in fig. 32 ; the 
southern Halleyan pole H^ is in this case the inaccessible 
one. We note first, that owing to the greater distance 
between i^ and Er the point of nearest approach to the 
pole Hi is still a long way from that pole. Moreover, 
we see that at Hg in fig. 33, the retardation of ingres> 



136 TRANSITS OF VENUS. 

and the acceleration of egress are less than the maximum 
by 4^ tenths, so that the total shortening is less than 
the sum of the maximum acceleration and retardation 
by fully 9 tenths of either. If the interval in time 
corresponding to the space between successive parallels 
were 1 minute, as we before for convenience assumed 
it, then in the case illustrated by fig. 32, the total 
shortening at the sunlit Halleyan pole Hg would 
amount to nearly 17 minutes, whereas in the case 
illustrated by fig. 33 the shortening at the sunlit 
Halleyan pole Hg amounts to little more than 11 
minutes. 

Thus, apart from geographical considerations, which 
may in some cases be of paramount importance, the 
applicability of Halley's method depends principally 
on the arc-distance between the tAvo Delislean poles in 
the northern hemisphere, which of course is equal to 
the distance between the Delislean poles in the southern 
hemisphere. 

This seen, it is easy to perceive that the first 
transit of a pair separated by eight years Avill be less 
suitable than the second. 

First take a pair of December transits like those 
of 1874 and 1882 — transits when Venus is at her 
ascendinof node. In this case the first transit alwavs 
carries Venus north of the sun's centre, as aloni? 
h V in Plate XI., while the second carries her south 
of the sun's centre as along s s ; for this being her 
ascending node, and the second transit finding her, as 
already explained, less advanced in her orbit, she is 



OF TEAIsSITS ASD THEIR COXLITIOXS. 1 37 

beyond her ascending node at the first transit and 
behind that point at the second transit — that is^ in north 
latitude in the former case^ and in south latitude in 
the latter. Accordingly, the centre of Venus's shadoAv- 
cone passes north of the earth as in fig. 21 in the case 
of the earlier transit of a pair at the ascending node, 
and south of the earth as in fig. 24 in the case ofthe 
later transit of such a pair. Thus the first contact is 
in the north-eastern quadrant as at i in fig. 22^ and 
the last in the north-western as at e fig. 23 ; and the 
point i on the earth having been carried round by the 
earth's rotation to the darkened side and (ren^embering 
the position of the earth's axis) on a course giving it 
a ofreater distance from e than it would have if the 
rotation were round an axis x s, we have the two 
Delislean poles farther apart than they would be but 
for the inclination of the earth's axis. Or we might 
have deduced the same result by considering the two 
poles I , fig. 22^ and e, fig. 23 ; for we see that the 
motion of / along its upward-bowed latitude-parallel 
is such as to give it a greater distance from e than it 
would have if the axis of rotation w^ere x s. But in 
the case of the transit of 1882, we see that i\ fig. 25, 
the place of second contact, is brought by rotation 
nearer to ^, the place of third contact,^ than it would be 
if the rotation were around an axis x s ; or we may 
infer the like by considering the relative motion of the 
northern Delislean poles i and e\ 

^ The reader should note that the effects here considered depend, 
entirely on the tilt of the earth's axis. 



138 TRANSITS OF VENUS. 

The position of the axis of rotation is then un- 
favourable to the earlier transit of a pair occurring in 
December. 

It will be easy for the student to apply similar 
reasoning to the case of transits occurring in June, as 
illustrated by figs. 27, 28, 29, 30, and 31 ; and it Avill 
be found in these cases also the rotation brings the 
Delislean poles (the northern pair or the southern pair) 
closer together, ccEteris paribus, in the case "of the later 
transit of a pair than in the case of an earlier transit.' 

But another circumstance clearly affects the dis- 
tance of the two northern, as of the two southern, 
Delislean poles. If the transit chord be shoii: as in the 
case illustrated by fig. 21, the points i and e^ (reference 
is now made to the small disc of fig. 21) will clearly 
be nearer tos^ether than where the transit chord is 
longer, as in the case illustrated by fig. 24 ; for the 
shorter the transit chord the greater is the angle 
enclosed between the intersecting: arcs 1 1 and e' e. 
Hence shortness of duration by tending to bring the 
two northern and the two southern Delislean poles 
close together renders a transit more favourable for 
the application of the method of duration. 

To see, lastly, how geographical considerations 
enter into the discussion of this problem, compare 
Plates VI. and VII., illustrating the transits of 1874 
and 1882. It will be seen that the northern or 



* The same is proved in another way in * The Universe and the 
Coming Transits,' — see also pp. 158, 159 of the present work ; and in 
yet another way at pp. 38 and 39 of my treatise on the 'Sun.' 



OF TRANSITS ASD TIIEIE COXLITIOXS. 1 39 

darkened Halleyan pole is nearly as far from the 
neighbouring sunlit region f for the whole transit) in the 
case of the former transit, as the southern darkened 
Halleyan pole is in the case of the latter transit. 
But the region Avhere such approach has to be made 
in 1874 is altogether accessible, though doubtless 
bleak and cheerless during the northern winter pre- 
vailing there when transit occurs ; whereas the sunlit 
region nearest to the southern Halleyan pole in 188*2 
is the inaccessible antarctic continent. Keeping away 
from that continent and within the space defined by 
the lines a b\ c d\ which show where the sun is ten 
degrees high at ingress or egress, there is absolutely no 
spot to be occupied which is near enough to h' to be 
Avorth the trouble of journeying thither. In both cases 
the region around the sunlit Halleyan pole affords many 
good stations, though the transit of 1874 is not i:i tliis 
respect comparable with that of 1882 ; but the absolute 
absence of any southern station whatever in 1882 
where the duration of transit i^ usefully lengthened. 
causes the method of durations to be wholly inap- 
plicable on that occasion. 

Thus far we have for simplicity considered the 
centre of Venus, or we may be said to have regarded 
Venus as a point. It is easy, hoAvever, to see what 
modifications are introduced when we take into account 
the fact that Venus is a globe. Thus, instead of a 
double cone, such as s s \ v v in fig. 20, having tlie 
centre of Venus at its vertex, we must consider tw(> 
double cones such as are shown in ficr. 34, each 



I40 TFcAXSITS OF VEXrS. 

enveloping both Venus and the sun. but one having 
its vertex outside the path of Venus (giving the shaded 
cone of the figure) and the other having its vertex 
within the path of Venus* It is manifest that any 
observer on the surface of the last-named cone, as for 
example, at v\ will see Venus touching the sun on the 
outside. i,e, in external contact; for the line of sight 
i/ V / touches both Venus and the sun, but on opposite 
sides, and is therefore directed to a point of contact o/i 
opposite sides of icliich the discs of Venus and the sun 
lie. On the other hand, an observer on the surface of 
the shaded cone, as on the prolongation of s \. will see 




Pig. 34. — liiustratiiig internal and external contacts. 

Venus just within the sun's disc, or in internal contact: 
for the line of sight touches both the sun and Venus 
on the same side, so that it is directed to a point of 
contact on the same side of which lie both the discs of 
Venus and of the sun. 

AVe see then that taking the two concentric circular 
sections v v fig. 34, we have only to substitute external 
contact and internal contact for what was said of the 
passage of the centre of Venus in the former case. 

In order, however, to still further familiarise the 
student with these fundamental relations, I shall aive 



OF TBAXSITS AXD THEIE COXDITIOXS. 141 

an independent description of the relations presented 
in fig. 34^ modifying into a more convenient form the 
explanation of the actual circumstances of the passage 
of the section of Tenus's shadoiv-cone (for so the v v^ 
of both fio;s. 20 and 34 may be regarded) over the less 
swiftly advancing earth. 

If an observer were carried through the double 
cone shown in fig. 34 beyond Yenus. he would see the 
following successive phenomena. When he came to 
the outer surface A'enus would be in exterior contact : 
as he passed on to the inner surface Yenus would 
enter more and more on the sun's disc, until when he 
reached the surface she would be in interior contact. 
Then as he travelled on through the inner cone Yenus 
would seem to cross the sun's disc, and she would just 
touch it on the inside when our observer reached the 
surface of this inner region on his passage outwards, 
Xext, as he passed onwards to the surface of the outer 
region, Yenus would be seen crossing the edge of the 
sun's disc. And lastly, as he passed that surface he 
would again see Yenus in exterior contact, the transit 
tliereupon coming to an end. 

During a transit of Yenus the earth does actually 
pass in such a way through these regions ; or rather 
these regions overtake and pass over the earth. 

Since the cones overtake the earth in the direction 
shown by the arrows, we may consider that the earth 
l^asses through the cones in the contrary direction. 

Suppose V V (fig. 35) to represent the same section 
of the outer cone as v v' in fio;. 34 ; v v' the section of 



142 



THAysITS OF VEXUS. 



the inner cone: and E (fig. 35) the earthy as sho^vn at 
E in fig. 34. Then v v is really moving towards the 
left; but we are to suppose that e is moving towards 
the rig:ht throuo;h v v\ Furthermore, if A^enus is 
near an ascending node, as she will be during the ap- 
proaching transits, we must suppose the earth to pass 
descendingly along such a course as E e' through the 
region v v\ The actual course, both as respects posi- 




Fig. ^ 



-Illu^tratiDO' internal and external contacts. 



tion and direction, is determined from the calculated 
elements of the transit. With this calculation we 
need not here concern ourselves.^ The fiorure shows 



1 As to the size of v v' and v v' compared \ntli that of the earth, it is 
easily seen from fig. 3-i that o v is greater and o vis less than the radius 
calculated in the note, p. 11-i for the centre of Venus, hv the radius of 
A^enus increased in the proportion that the earth's distance from the sun 

exceeds the distance of Venus from the '^un. 



J 



OF TRANSITS AND THEIR CONDITIONS. 1 43 

the course actually traversed by the earth in 1874 and 
1882. 

Now^ taking the earth through v v^ for the 1874 
transit^ let us consider the various critical points^ so to 
speak, of her course. When she first touches the 
outer circle v v^ external contact will have beo:un at 
that point of the earth which first reaches this circle. 
She passes on, falling more and more within v v ^ until 
she is just wholly within. All this time external con- 
tact is taking place w^herever the outline v v^ intersects 
the earth's disc; at parts within that line Venus is 
seen partly within the sun's disc^ and at parts outside 
of it external contact has not yet taken place. When 
the earth has passed wholly within the circle v i'\ 
external contact has taken place at all parts of the 
visible hemisphere. But as at this time no part of the 
earth has reached the circle v v^,^ internal contact has 
nowhere commenced. In other words, Venus is not 
yet fully upon the sun's disc as seen from any part of 
the earth. 

Now, this part of the earth's motion is not illus- 
trated in fig. 35, because external contacts and the 
passage of Venus across the sun's outline are not 
phases to which the observers of transits pay great 
attention. We now come to the important phases. 

^ The distance between the circles v v' and v v' is obviously greater 
than the earth's diameter, if we consider how the two circles v v' and 
V v' are obtained. For the diameter of Venus is very nearly equal to 
the earth's ; so that the diverging lines from 5 or 5' (fig. 34) are already 
separated at v by a distance nearly equal to the earth's diameter, and 
therefore at v or v' are wider apart. 



144 TIlAySITS OF VFXUS. 

When the earth just reaches the inner circle v y\ 
interior contact has just begun at the point on the 
earth which first touches this circle. Here, then, 
earliest of all, internal contact begins, and we have at 
this point the phenomenon called by astronomers Ji?\^t 
internal contact most accelerated,^ The earth is then 
in the position numbered 1 in fig. 35. 

She passes on, the outline v v^ encroaching more 
and more over her face until she is wholly within this 
outline or in position 2. All this time internal contact 
is taking place wherever the outline vv^ intersects 
the earth's disc. At parts of the earth within that 
line internal contact has passed, or Venus is already 
fully upon the sun's disc. At parts of the earth out- 
side that Ime Venus still breaks the outline of the 
sun's disc. When the earth is at 2, internal contact 
has taken place for all places on the earth's illuminated 
hemisphere. This contact takes place latest of all at 
that point on the earth's surface which at this moment 
touches V v\ It is here, then, that there occurs the 
phase which astronomers Q^iWjirst internal contact most 
retarded. 

Then the earth passes onwards through the posi- 
tions shown severally along her track in fig. 35. 

As the earth passes out of the spaces v t', v c , 
similar phases occur in reverse order. We need note 
only the positions numbered severally 14 and 15. 
The first shows where the earth first reaches v v', and 
the point on her surface which first touches v v^ is the 
place where occurs the phase called second internal 




: \ \ ^, ^ 


\ \ \ \ v^ 


^^S 


w.. 


:-....-.. Pro cLor. dei^ 




IVli.Giii. 30 s. 





OF TRANSITS AXB THEIR CONDITIONS. 1 45 

contact most accelerated \ while 15 shows where the 
earth is just passing clear of vy", and the point on 
her surface which is the last to touch Y Y^ is the place 
where the phase occurs called second internal contact 
most retarded. The circumstances of the progress of 
the earth from one position to the other precisely 
correspond to those already considered in dealing with 
the earth's motion from 1 to 2^ only they take place in 
reverse order. 

Plate XVI. illustrates the progress of the earth 
within Venus's shadow-cone during the transit of 
1874^ through the positions marked 1^ 2^ ... 14^ 15, 
in fig. 35. The path of the earth in this figure is, for 
convenience of engraving, broken up into three parts, 
shown in fig. 36, and the earth is represented at each 



5 6 7 8 9 ID 11 



Fig. 36.~Explaining Plate XYI. 

part of her progress^ precisely poised and rotated, as 
she would appear if she could be viewed from the sun 
during the course of the transit of 1874. 

Leaving the cross-lines out of consideration for the 
present, let the student study this plate^ interpreting 
it by reference to figs. 34 and 35, and he will be able 
to form more exact conceptions of the real relations 

L 



I'ASSAC.K OK TIIK V.lWnW TIlHOI'Cll VKNUS'S S11.\IM)W ( OM 1)1( 8 18' 




146 TRANSITS OF VENUS. 

presented during the transit than he could from a long 
and recondite explanation. He sees in the first picture 
of the earth those regions whence the beginning of 
the transit will be visible. He sees in the last those 
regions where the end will be visible. Those parts of 
the earth which appear in both these views are those 
from which the whole transit will be visible. And, 
finally, those parts which do not appear in either of 
these views (nor, therefore, in any of the fifteen) are 
those whence no part of the transit will be seen. 

Plates XVII. and XYIII. represent the earth as 
supposed to be seen from the sun at the beginning 
and end of the transit. 

Of these views the first represents the earth as she 
would appear from the sun when her centre is just 
crossing the circle v v^ of fig. 35 at ingress, and the 
second represents her as she would appear when her 
centre is just crossing the same circle at egress. So 
that the first corresponds to an epoch between those 
represented in the first two earth-pictures of the fold- 
ing plate, while the second corresponds to an epoch 
between those represented in the last two pictures of 
that plate. The seemingly parallel cross-lines in 
Plate XVII. represent the encroaching outline of the 
circle v v^ (fig. 35) at intervals of a single minute of 
time between the epochs represented by the first two 
figures in the folding plate. The corresponding cross- 
lines in . Plate XVIII. represent the same outline 
gradually passing off the earth's face between the 
epochs corresponding to the last two figures in the 



OF TRANSITS AND THEIR CONDITIONS. 1 47 

folding plate. The encroachment and the passing off 
not being strictly uniform,^ these lines are not equi- 
distant, nor are they strictly parallel or straight. 

These two plates have been given merely to illus- 
trate the exact constructions which can be applied to 
such projections, in order from them to ascertain the 
best stations for applying various methods.^ They 
have been reduced by photolithography from two of 
the quarto plates illustrating ^ The Universe and the 
Coming Transits.' For general descriptive illustra- 
tion. Plates XII. and XIII. are more suitable, as 
simpler and clearer. Since at present I am not deal- 
ing with the special conditions of the coming transits, I 
need not here discuss the geographical details of these 
plates, or of plates XIV. and XV. illustrating the 
transits of 1882. 

1 The reason of this will be seen by a reference to fig. 35. Obviously 
the rate at which the earth's centre is approaching the centre of Yenns 
(which rate really measures the rate of encroachment) diminishes during 
ingress, while for a like reason the rate of passing off increases during 
egress. 

2 Properly speaking Plates XVII. and XYIII. only represent the 
earth accurately for the moment when the outline of y V (fig. 35) 
crosses the earth's centre. Since, as we see by the cross-lines, no less 
than 25m. 6s. are occupied by the passage of the outline of y y' over the 
earth's face, both at ingress and egress, the earth's rotation has to be 
considered. This, however, can very easily be done, since the latitude 
circles are shown, and the longitude circles are separated by ten degrees, 
corresponding to the earth's rotation in forty ' minutes. Thus from 
Plate XYII. we see that the cross-line marked 7m. on the right of the 
centre passes near Jeddo. But as the cross-line occupies this position 
seven minutes before it crosses the Earth's centre, we must put Jeddo 
back through an amount corresponding to seven minutes' rotation, or 
about one-sixth of the distance separating two longitude-circles in this 
neighbourhood. 

L 2 



]48 TRAXSITS OF VEXrS. 

But n(n\% lastly, it remains to show how the actual 
progress of a tran:^it as seen from the earth corre- 
sponds with the progress of the earth through Venus's 
shadow-cone as illustrated in figs. 34 and 35. For 
although the plan of dealing with tlie problem by 
considerino; the loassao-e of the earth throuoh these 
cones is, on the whole, the most convenient which can 
be adopted, and especially on this account, thnt it shows 
js directly what face of the earth is turned sunwards 
at the beginning or end or at any other stage of the 
transit, yet there is something artificial in this way of 
considering the subject. The student who wishes 
to know what can actually be seen from the eai'th 
seeks for something more than a description of what 
mi_ht be seen from the sun under certain imagined 
conditions. 

A very simple consideration will enable us at once 
to transpose the relations illustrated in fig. 35 in snch 
a way as to correspond to the actual transits across 
the solar disc. 




Fig. 37. — Illustrating the connection between the passage of "^ enus over 
tile sun's face, and the passage of the earth through Venus's shado^-coue. 

Suppose s (fig, 37) the sun's centre, s ^ s a dia- 
nietral plane of the sun square to the line s v o^ which 



OF TRAXSITS AND THEIR COXDITIOXS. 1 49 

forms the axis of the shadow- cones we have been 
dealing with (for simplicity taking the cone as in fig. 
20). Thus 5/ is a circle directly opposite to vv\ the 
planes of these circles being parallel. (The left-hand 
halves of the ovals / s and v v^ are supposed to be the 
nearer.) j^ow imagine a straight line passing through 
V to the centre of the earth E on one side^ and to the 
circular disc s s on the other. Since the earth's centre 
carrying this line travels along E e' athwart v v^ on the 
path ie, such as is shown in fig. 34, passing slantingly 
downwards below the centre of v v\ it is clear that the 
other end of the line will travel along f f^^ across s /, on 
the path a 65 moving slantingly upwards above the centre 
of s s. If we looked at v v^ from y, the motion of the 
earth would be from left to right along ic ; and mani- 
festly, if we looked at s s from v, the motion along a h 
would also be from left to right. In other words, 
whereas g^6, as a projection of ie, is inverted, it is not 
reversed right and left, provided we are supposed to 
view V v^ and s s\ in turn, from the point V. The 
chord a b, then, so viewed, is a perfect projection of 
^ e, inverted without being reverted right and left. 

And clearly this principle of projection may be 
extended to all that is pictured in fig. 35, not only as 
respects motion along the transit chords of 1874 and 
1882, but also as respects the sun- views of the earth 
supposed to be presented by the numbered discs, and 
actually presented on a much enlarged scale in Plate 
XVL The circle s /, of fig. 37, which represents the 
solar disc, is a perfect projection of v v^ in this sense. 



ISO TRANSITS OF VENUS, 

that wherever an observer be supposed to be placed 
on the circle v v\ he would see the centre of Venus 
projected at a point of s s^ corresponding to his own 
position, only inverted as respects north and south. 
And if we imagine a small figure of the earth properly- 
placed on the chord i e^ with correct pose of axis and 
rightly rotated, to correspond to the time at which the 
earth actually reaches that part of i e^ then for every 
point on the sunlit-half of that small globe there will 
correspond a point on s s\ If, further, we imagine a 
straight line extending from V to this globe of the 
earth on one side and to s / on the other, and that the 
former extremity is carried along all the outlines of 
continents and islands on the sunlit-half of the globe, 
the other extremity will describe on the disc s / an 
inverted, but not reversed, picture of those continents 
and seas. Any point in this inverted picture will indi- 
cate the point on the sun's disc occupied by the centre 
of Venus, as supposed to be seen at the corresponding 
moment by an observer placed at the corresponding 
point of the earth's globe. So that when once we 
have constructed such a picture as Plate XVI., giving 
a series of sun-views of the earth during her passage 
through the sections v v\ \Y^ (fig. 35), of the shadow- 
cones shown in fig, 34, we have at once the means of 
determining the apparent path of Venus's centre 
across the sun's disc for any station whatever upon 
the earth. In fact, Plate XVI., held up to the light, 
inverted, and looked at from behind, pictures the por- 
tion of the sun's disc traversed by Venus ; the pictures 



THE TRANSIT OF , centre 




1. Kerguelen Land.. 

R. A. Proctor, deU 



2. Possessii T.Delll 



OF TRANSITS AND THEIR CONDITlOyS. 151 

of the earth inverted without reversion are such pro- 
jections as I have been speaking of; and we have 
only to dot down the place of any island or town in 
these successive projections^ and to connect the succes- 
sive dots by a line^ to have the path of Venus's centre 
across the sun's disc as viewed from that island or town 
during her passage. 

Plate XIX. has been constructed in the way here 
indicated^ only that I have thought it better to show 
projections separated throughout by a quarter of an 
hour^ instead of having internal contacts (most accele- 
rated and most retarded) illustrated specially as in 
Plate XVI. Plate XX. is intended to explain more 
clearly the meaning of Plate XIX. It shows the 
northern half of the sun's disc. Outside and inside 
this disc are circles^ one having a radius exceeding the 
sun's by Venus's semidiameter^ and the other having 
a radius less than the sun's by the same amount ; so 
that when Venus's centre crosses the outer circle her 
outline just touches the sun's on. the outside, or she is 
in external contact, while when her centre crosses the 
inner circle her outline just touches the sun's on the 
inside, or she is in internal contact. Parts of these 
circles are shown in Plate XIX. Across the disc five 
parallel lines are drawn. The central one is the path 
of Venus's centre supposed to be viewed from the 
centre of the earth. The line next to the centre, 
above, shows the path of Venus's centre supposed 
to be always so viewed from a southerly station as 
to be thrown as far as possible from the central 



HE TRANSIT OF VENUS IN DECEMBEP 1^74 S 



SHEV INC THE PATH OF VENUSS CENTRE ACROSS THE DISC OF THE SUN AS SEEN FROM THE FOLLOWING TWELVE STATIONS 




152 TRANSITS OF VENUS, 

path on the northern side;^ and the line next to the 
centre, below, shows the path of Venus's centre as sup- 
posed to be always so viewed from a southerly station 
as to be as far as possible from the path of the central 
path on the southern side. The lines next outside the 
two last-mentioned mark the boundaries of the track of 
Venus's disc as supposed to be seen from the centre of 
the earth. And lastly, the outside dotted lines mark 
the northern and southern boundaries of the tracks pur- 
sued by Venus's disc if so viewed that her centre w^ould 
follow the tracks shown north and south respectively of 
the central path. No part of Venus can be seen^from 
any part of the earth, outside these dotted lines. 

In Plate XIX., the tracks followed by Venus's 
centre as seen from twelve important stations, are 
marked in. The student can readily add, either on 
the plate itself or on a tracing from it, the transit path 
for any other station. It will be found a useful exer- 
cise to trace from Plate XIX. the central path and 
the outline of the sun's disc, and the path of any 
stations whether of the tw^elve dealt with in the plate 
or such others as the student may desire, and then 
having cut the picture thus formed into three parts by 
horizontal lines (where the black spaces fall in the 
plate) to connect them into one long strip correspond- 
ing to the transit band of Plate XX. 

^ There is no fixed point in the earth where this relation -^onld hold. 
The observer would have to be placed at the point of the earth which 
just touches the southern transit-parallel in Plate XVI., and this is a 
point continually travelling backwards along a southern latitude -parallel. 
A similar reraark applies to the corresponding northerly positions. 



path cii tlu )n,idu:i}i side;' and the line next to the 

Cf litre, below, shows the path of Venus's centre as sup- 

ed to be always so viewed from a southerly station 

s possible from* the path of the central 

tiie southern side. The lines next outside the 

luij iH<t-mentioned mark the boundaries of the track r^ 

Venn-''? (U^r as supposed to be seen from the centre oi 

J lastly^ the outside .dotted lines mark 

the no J i southern boundaries of the tracks purr 

sued by v er u^ s disc if so viewed that her centre wouM 

fVHowthe tracks Siiow^^ Vvydh and south respective! v.. k' 

f Venus can be seen. 
sn dotted line 
i^v.j tne rracKs followed by > euus's 
f^oD'^ t^'M]%^5- ivn\')rTnn^ ^^^^iHons, are 

aither* on 

, the transit path 

lor any otiier -^uxi^jii. it: w^iii be lound a useful exer- 

-isf' to H:\o.9. rroin Plati= TTX, the centriil path an^' 

he sur nd the path of an 

ealt with in the. plate 

bucb v^Lhers as Lhe stucieiit may desire^ and then 

ving cut the picture thus formed into three parr- 1.. 

i ori^ontal line?? (where the black spaces fall iu 

p]p ong strip correspond- 



■,o io ViO flxvv^ pCiLt. lii clie <iartxi vv'lieicj this relation woiiIJ hold. 

•-er would have to be placed at the point of the earth which 

c^ southern transit-parailel in Plate X^H!., and this is a 

r ^^??T■pV^!^'? bn.c^r^p."rd? filoTijT n scithrm I'ttitii^^ "r!?>TTill<?l. 



OF TRANSITS AND THEIR CONDITIONS. 153 

It remains only to be added that the process applied 
in the construction of Plates XVI. and XIX. to illus- 
trate the transit of 1874, can easily be applied to any 
other transit. Take for instance the transit of 1882. 
Here a portion of the work has been already donCj 
since Plates XIV. and XV. illustrate the beginning 
and end^ Avith the position of the circles v Y^ of fig. 35. 
A picture of the space enclosed between the transit 
chords for 1882 fig. 35, and the circle Yv' ought to 
be made on such a scale that the distance between the 
transit chords would equal the diameter of the discs in 
Plates XIV. and XV. Or, if that scale be too large, 
then figs. 38 and 39 may be used instead. A series 
of sun-views can readily be drawn on tracings of the 
meridians and parallels either of Plates XIV. and 
XV., or of figs. 38 and 39, corresponding to successive 
equal epochs (say fifteen minutes apart) all through 
the transit. These must be arranged in a row as in 
Plate XVI., in their proper order, and so posed that 
the central cross-lines (marked mean time in Plates 
XIV. and XV., and 0^ in figs. 38 and 39) may cross 
the track of central transit at the equal angles at which 
the circle yy^ crosses that track in fig. 35. Then 
will a picture corresponding to Plate XVI. have been 
constructed, except that internal contacts will not have 
been specially illustrated by projections corresponding 
to these contacts (as most accelerated and most re- 
tarded). The picture so drawn, if inverted and looked 
at from behind (or if inverted and viewed in a mirror), 
will correspond to Plate XIX., and enable the student 



154 



TRANSITS OF VENVS. 



to trace the path of Venus's centre as seen from any 
station whatever on that occasion. 

Other transits may be illustrated with equal 

TEANSIT OF 1882. (INGEESS.) 



Retarded 
Ingress 




Accelerated 
Ingress. 



Fig. 38. — Illuminated side of the earth at ingress, Dec. 6, 2h. 15m. 56s. 
(Greenwich mean time.) 

readiness. Nor need the details of the process be any 
further illustrated by examples^ since any student who 
takes sufficient interest in these matters to attempt the 
projection of a transit in the manner here applied to 
the approaching transits^ will have sufficiently examined 
the earlier portions of this chapter to be able to recog- 
nise clearly the relations involved in constructions of 
the kind. 



OF TRANSITS AND THEIR CONDITIONS. 155 

The construction of such illustrative projections as 
Plates II., III., &c. . . . IX., needs no explanation ; 
for these are simply stereographic polar projections 



TKAXSIT OF 1882. (EGEESS.) 



O^ \ \ \ \ ^ ^ 




Fig. 39. — Illuminated side of the earth at egress, Dec. 6, 8h. Om. 82s. 
(Greenwich mean time.) 

of the earth, upon which various lines and points, 
obtained by the methods already described, are laid 
down for convenience of study and reference. 



156 TJ?AX.siTS OF ri:yus. 



CHAPTER V. 

THE COMIXG TBAXSITS. 

The discovery that the sun's distance^ as determined 
by Encke from the transits of 1761 and 1769^ was con- 
siderably in excess of the truths naturally directed 
special attention to the transits of the present century. 
It was in 1857, only three years after Hansen had 
announced to the Astronomer Royal the correction in 
the sun's distance resulting from the lunar theory, 
that Sir G. Airy first called the attention of astrono- 
mers to the subject of the approaching transits, and to 
the inquiry how the opportunities presented by these 
transits might best be employed. In a lecture 
delivered before a meeting of the Astronomical Society 
in May 1857, he examined the various methods avail- 
able for determining the sun's distance, and ascribing 
to the observation of Venus in transit the highest 
value, he considered in a general way the circum- 
stances of the transits of 1874 and 1882. He pointed 
out that, cceteris paribus, the second transit of a pair is 
superior to the first for Halley's method ; but unfor- 
tunately failed to observe that special circumstances 
may modify or even reverse this relation. Although. 



THE COMIXG TRAXSITS. 1 57 

I have given one demonstration (in the preceding 
chapter) of the general law and of the fact that the 
coming transits present an exception to it^ it will be 
well to show here the nature of Airy's reasoning : — 

Let fig. 40 represent the face of the earth as sup- 
posed to be seen from the sun during a December 
transit, such as either of the approaching transits. 
Kow, the earth durino; the transit is mo vino; from ris^ht 
to left^ or in the direction shown by the long arrow 
(the slant of the axis is for simplicity neglected). 
Her rotation shifts points on her surface in the way 
shown by the small arrow on the equator, the shift 
due to this cause being greatest on the equator. This 
motion manifestly takes place in a sense adverse to 
that of the earth^s motion of revolution, everywhere 
except at stations on the sliaded lune of the disc. 
Xow, Venus transits with the excess of her motion of 
revolution over the earth's: and anything which tends 
to reduce the effects of the earth's motion of revo- 
lution, increases the excess of Venus's motion- -or in 
other words, hastens A^enus in her transit. So that at 
every point of the unshaded portion of the disc in 
fig:. 40 Yenus is hastened, more or less, bv the effects 
due to the earth's rotation. On the contrary, at every 
point on the shaded portion of the disc Yenus is 
retarded in her transit. 

These circumstances affect diversely the two transits 
of such a pair as we are now awaiting. If fig. 41 
represents the sun's disc, the north point being upper- 
most, then the lines ab^ c rZ, will represent chords of 



158 



TRANSITS OF VENUS. 



transit in 1874 {ab being the chord for a northern, c d 
being the chord for a southern station) ; and a! h\ 
c d! will represent chords of transit in 1882 {o! V beino* 
the chord for a northern, c' d' the chord for a southern 
station). 

It is manifest that in 1874 the conditions affecting 
the duration of the transit as seen at a northern station 




Fig. 40. — Illustrating the effect of the earth's rotation on the progress 
of a transit. 

are adverse. The chord a b is longer, owing to the 
northerly latitude of the observer ; but Venus is 
hastened on her course, and therefore the lengthening 
is not so great as it otherwise would be. We have 
then one favourable and one unfavourable condition, 
the latter to some degree cancelling the former. (In 
some transits of the kind the effect of rotation wholly 
cancels, or even more than cancels, the effect due to 
latitude.) The southern station, if taken where. 



THE COMIXG TRAXSITS. 



1 59 



throughout the transit^ the observer is on the portion 
of the disc represented without shading in fig. 40, will 
give conspiring effects. The chord of transit c d mil 
be shortened, and Yenus will be hastened on her 
course. Hence we have for this station two favourable 
conditions. In all we have three favourable conditions 
and one unfavourable condition — so that if the con- 




Fig. 41. — Illustrating the effect of the position of transit chords. 

ditions are all equal in value we have a balance of only 
two favourable conditions. 

On the other hand, in such a transit as that of 1882 
we can theoretically secure four favourable conditions. 
We have at the northern station the shortened transit 
chord a^ h\ and a hastening of Venus — or two conspir- 
ing conditions. At a southern station we have the 
lengthened transit chord c^ d! ^ and by taking a station 
which throughout the transit lies on the shaded part 



l6o TEAXSITS OF VFXUS. 

of the disc (that is, an Antarctic station passing below 
the pole during the transit hours), we have Venus 
retarded on her transit path, or again we have two 
conspiring conditions. In all, then, we have four 
favourable conditions, or twice as many as we obtain 
for the bahmce of favourable conditions in 1874. 

This is theoretically sound. Moreover, it is quite 
commonly the case that the effects due to rotation are 
equivalent to those due to latitude, and that therefore 
the adverse conditions at a station placed as the 
northern station in 1874 may be regarded as cancelling 
each other. In the transit of 1769, for example, the 
conspiring effects of rotation and latitude were nearlv 
equal. The Astronomer Royal, in his ^ Popular 
Astronomy * (published in 1848, be it noticed), justly 
assigns to rotation 10 minutes out of the observed 
maximum difference of duration, 22 minutes. It does 
not seem rash to infer that he had this result in his 
thouolits when, after mentionino: that the best northern 
stations would probably not be occupied in 1874, he 
proceeded to remark (in 1857) that the ' observahlp 
difference' in the earlier transit icoidd ' probabhj not 
he half of that in 1882.' 

Although the observable difference in 1874 is reallu 
half as great again as in 1882, yet it mattered very 
little, at that early epoch, if any mistake of this sort 
crept into what claimed to be little more than a popular 
account of the general subject of transits. Xo one 
probably considered that the Astronomer Royal 
attached any weight to the details of his paper of 1857. 



THE COMIXG TBAXSITS. l6l 

In fact, so roughly ^vas the paper prepared that the 
time of mid-transit in 1874 was an hour wrong — an 
error not resulting from incorrectness of the tables, for 
the time of transit of 1882 was very nearly correct. 
In fact^ the paper of 1857, accurate enough for its 
purpose^ had not^ and did not seem intended to have^ 
any scientific weight. 

But unfortunately, the Astronomer Eoyal^ when 
next he dealt with the subject, seems to have regarded 
the transit of 1874 as demonstrated by his former rough 
paper to be unfit for the application of Halley's 
method. For. in 1864, he published a sufficient! v 
accurate investigation of the transit of 1882. illustrated 
by projections (corresponding to those forming Plates 
VI. and YII.) well executed by Mr. H. Carpenter of 
Greenwich, and in this paper the transit of 1874 was 
not considered at all. In 1865. he again commented 
on the circumstances of the transit of 1882 without 
mentioning the earlier transit. AVhen at length, in 
1868, he published what purported to be a detailed 
description of the circumstances of the two transits. 
and of the duties not of English astronomers only, but 
of astronomers generally with respect to the transits, 
he remarked that Halley's method had been sltoicn to 
fail totally in 1574. 

It will serve, I think, to remove misconceptions if 
I quote here the remarks addressed to the scientific 
world by Sir George Airy in 1868 respecting the 
important transits of 1874 and 1882. 

^On two occasions,* he writes, ("'Monthly Xotices/ 

M 



1 62 TRANSITS OF VENUS. 

1857, May 8, and 1864, June 10) '1 have called the 
attention of the Society to the transits of Venus across 
the sun's disc, which will occur in the years 1874 and 
1882 ; and have pointed out that, for determination of 
the difference between the sun's parallax and the 
parallax of Venus, the method by observation of the 
interval in time between ino;ress and eo:ress at each 
of two stations at least, on nearly opposite parts of 
the earth (on which method, exclusively, reliance was 
})laced in the treatment of the observations of the 
transit of Venus in 1769),^ fails totally for the transit 
of 1874, and is embarrassed in 1882 with the difficulty 
of finding a proper station on the almost unknown 
Southern Continent. 

' The publication of M. Le Verrier's new Tables 
of Venus, and of Mr. Hind's inferences from them as to 
the points of the sun's limb at which ingress and egress 
will take place in each transit (which inferences I have 
in part verified), has induced me again to examine the 
Avhole subject. And, without giving up the hope of 
using the observation of interval between ingress and 
egress at each of two stations in 1882, I have come to 
the conclusion (from all the information which has 
reached me) that it will be unsafe to trust exclusively 
to the chance of securing observations on the Southern 

^ As it has been said (as a correction of my own criticism of the 
above paper) that Sir Gr. Airy did not describe the ' method of durations ' 
as failing totally, but only Halley's method, meaning the method of 
durations as ajyjplied, to a nearly central transit, I invite special attention 
to his careful wording. The parenthesis removes all doubt as to his 
real meaning (for the transit of 1769 was far from central}; though in- 
deed without the parenthesis the meaning is unmistakable. 



THE COMIXG TRANSITS. 1 63 

Continent; and that, while observations are by all 
means to be attempted in that manner, it is also very 
desirable to combine with them observations of the 
same phenomenon (at one time the ingress, at another 
time the egress), made at nearly opposite stations 
whose longitudes are accurately know^n, and recorded 
in accurate local time. This principle being once 
admitted, the transit of 1874 is, or may be, as good 
for observations of that class as the transit of 1882; 
and the selection of localities for the observations must 
be made with equal care for the two transits.' 

He then explains how the maps wdiich illustrate 
his paper were constructed, and proceeds to discuss 
the individual maps Avith reference to the selection of 
stations for observing the several phenomena. Plate 
VI. will serve as well as these maps to illustrate what 
follows: — 

L — ^ Stations for observing the Ingress as accelerated 
hy Parallax'' — that is, Stations near \ {Plate VI.) on 
the Illuminated side of A B, but not too near to A B.^ 

^ Owhyhee and the neighbouring islands are excel- 

' If 10° be assumed as the lowest elevation at whicli -useful obser- 
vations can be made, then the stations must not lie within 10° of the 
circle A B. The arcs « ^, c cZ, ft' (^', c' c^', Plates VI. and VII., indicate 
this limit for the transits of 187'! and 1882. Thus a station for 
observing ingress accelerated by parallax (in 1874) should not be 
anywhere within the zone a b /; « ; so that the best point for observing 
accelerated ingress would be that point on a b which lies nearest to i. 
Similar remarks apply to observations of retarded ingress near 1', of 
accelerated egress near e', and of retarded egress near e, the dotted 
curves a' b' , c' cV, and c (^marking the limits outside which stations should 
be placed. 

M 2 



1 64 TRANSITS OF VEX VS. 

lent. The factor of parallax ^ is about 0*92, and the 
sun is at nearly two hours' elevation. There is English 
society at Woahoo. These islands are just Aviihm the 
tropics. For use of this station the absolute longitude 
must be accurately determined. 

^ At the Marquesas Islands the factor of parallax 
is 0*7^ and the sun is nearly as high as at Woahoo. 
Our neighbours across the Channel have^ from the 
tii]ie of Louis XIV.^ taken an honourable lead in 
scientific enterprise of every class. I trust that we 
may rely on them for accurate determination of longi- 
tude at Marquesas^ and for accurate observation of the 
ingress in 1874. 

' The desert Aleutian Islands can scarcely be recom- 
mended, although the factor 0*8 for the westernmost of 
them^ where the sun is highest^ is favourable. But 
it is very probable that the Russians will soon have 
established telegraphic communication with the mouth 
of the Amoor, by which its absolute longitude will be 
accurately determined ; and though the factor is only 
KYdI , the sun is 15° high^ and the station will be valu- 
able. 

' On the whole, if the British Government will 
undertake the accurate determination of longitude of 
AVoahoo, and the careful observation of ingress there 
in 1874, w^e may consider that good provision is made 
ibr the accelerated ingress.' 

^ This expression indicates the acceleration or retardation at the 
station, regarding the maximum acceleration as unity. 



THE C O:\liyG TFiAXSITS. 1 65 

II. — • Stations for ohservin^^ the Ingress a^^^ rpfarded Inj 
Pa ra llax ' — tJi a t is, St a tion .^^ n ca r l' il 'la ie yi,\ </ii 
the lUiimi noted side of A^ B , hyi not too near to a' ^\\ 
See note, p, 163. 

' The best station, as referred to the test of numbers. 
is Kerguelen's IsLand, where the factor is 0*91. and tlie 
sun is 25^ high. This island is emphatically known 
as '• The Island of Desolation." I know not whether 
its character is so repulsive, or its ntility as a zero oi 
longitude so small, as to make our nautical authorities 
unwilling to determine its longitude, and to siaiion 
observers there in 187-i. If these difficulties are not 
thought too great, it will be an excellent position. At 
Crozet's Islands the factor 0*98 is very favourable^ but 
the sun is rather low (10^ altitude). 

' The next stations in order of merit are Rodriguez, 
Mauritius, and Bourbon. Mauritius possesses this 
claim, that it will be a fairly good station, though not 
so good as Bourbon, in 1882.; in 1874 as well as in 
1882, it has this disadvantage, that the sun will be 
low. If only one longitude can be determined in this 
chain of islands, it ought to be that of Mauritius : if 
two can be determined, they ought to be those of 
Rodriguez (for 1874) and Bourbon (for 1882). 

^ At Madras and Bombay the factors, 0*47 and 0*44, 
are small; but the value of either station does not 
depend entirely on its simple factor, but upon the sum 
of its factor with the factors at the stations under 



1 66 TRANSITS OF VEXUS, 

head I. These two observatories^ with well-known 
longitudes^ will prove very useful stations. 

* With the assistance which we may hope to 
receive from the British Government, we may con- 
sider the observation of the retarded ino;ress as well 
secured.' 

III. — ' Stations for observing the Egress as accelerated 
hg Parallax ' — that is, Stations near e' {Plate VI.) on 
the Illuminated side ofo! \)\ hut not too near to o! v>' , 
See note^ j). 163. 

' Excluding from consideration the Southern Conti- 
nent as not to be entertained in our thought with- 
out the most absolute necessity, the stations in order 
ot merit are the Auckland Islands, Canterbury, 
Wellington, and Auckland, in Xew Zealand (factors 
rangmgfrom 0*83 to 0-77), Norfolk Island (0-66), Mel- 
bourne and Sydney (0*6). I omit Chatham Island, 
where the sun is rather low. The existence of the 
observatories at Melbourne and Sydney makes the 
observation of the accelerated egress almost secure, 
although, in confirmation, I should much desire to 
have one station at least on the Xew Zealand group.' 

IV. — ^ Stations for observing the Egress as retarded bg 
Parallax"' — that is^ Stations near E {Plate VI.), on 
the Illuminated side of C D, but not too near to C D. 
See note, j), 163. 

' The stations which are favourable for this ob- 
servation are almost entirelv on Russian and Turkish 



THE COMING TRANSITS. 1 6/ 

territories. At none of them is the factor less than 
0*84 ; and we have^ therefore, only to consider the 
elevation of the sun, leaving to the national Grovern- 
ments to estimate the facilities or difficulties depend- 
ing on the locality, the climate, or the season. Any 
station either to the east or to the west of the Lower 
Caspian will have the sun well elevated. Omsk, Orsk 
(whose longitude has been determined with peculiar 
care), Astrakhan, Erzeroum, Aleppo, Smyrna, and 
Alexandria, have the sun sufficiently high. At 
Tobolsk, Perm, Kazan, Kharkov, Odessa, Constanti- 
nople, and Athens, the sun will be rather low, and at 
Moscow it will be on the horizon. ^Ye may, with the 
utmost confidence, leave the selection of the stations, 
the determination of longitude, and the observation 
of the phenomenon, to our Russian friends.^ One 
station, however, ought specially to be considered as 
being, for this purpose, in British hands, namely, 
Alexandria. It appears not improbable that we may 
soon have very direct telegraphic communication 
^^T.th Alexandria; but, failing this, I trust that no 
efforts will be wanting to determine accurately its 
lono-itude — a lono-itude which was in the survev of 
Admiral Smyth, and which always must be, the 
zero of lono-itude in the Levant. This beino; as- 
certained, Alexandria would probably be the best 

^ It cannot but be manifest from the wbole tone of this passage that 
the conditions of the transit for the scientific world, and not for British 
astronomers only, were intended to be presented in the Astronomer 
Kojal's paper. 



1 68 TRANSITS OF VEXUS, 

of all the stations for observation of the retarded 

ss.'i 

Transit of Vexus, 1882, December 6. 

First, by the Method of Absolute Longi- 
tudes. 

V. — ' Stations for ohserving the Ingress as accelerated 
btf Parallax ' — that is, Stations near V {^Plate VI L), 
on the Illuminated side of A^ B^, hut not too near to 
a'b^ See note, p, 163. 

' Omittmg for the present all allusion to the 
Southern Continent, it will be seen that the best 
station is Kerguelen's Island, its factor being 0*98, 
and the sun's elevation (12°) probably sufficient. 
This circumstance, in addition to its value as ex- 
plained in the discussion of Plate II., renders it well 
worthy of attention. At Crozet's Islands the factor is 
0-9, and the sun's elevation 23°; abstractedly it is 
preferable to Kerguelen's Island, but not in quite so 
great a degree as that in which Kerguelen's Island is 
superior in list II. The next in value are Bourbon 
and Mauritius, with factor about 0*78, the sun 
being higher at Bourbon. On comparing these quali- 
lications with those remarked under head II., the reasons 

^ The absolute omission of the Indian stations here, though they 
had been mentioned among those nseful for observing retarded ingress, 
is remarkable, bnt is readily understood when the Astronomer Eoyars 
maps are examined. North India is nearer to e (Plate YI.) than Alex- 
andria, and has a higher sun. 



THE COMING TRAXSITS. l6g 

will be evident for my recommendation that either 
the lonofitude of Mauritius or the lono;itades of Bourbon 
and Rodriguez should be determined. 

' At the Cape of Good Hope the factor is about 
0*625 and the observation there will be valuable. 

* The satisfactory observation of the accelerated 
ingress requires, however, some longitude-determi- 
nations.' 

VI. — ^ Stations for observing the Ingress as retarded hg 
Parallax'' — that is^ Stations near i {Plate VIL), on 
the Illuminated side of A B, hut not too near A B. 
See note^ p, 163. 

^ Every city near the seaboard of the United States 
of America, and every important city of Canada, 
commands this phenomenon most favourably. The 
lowest factor is 0*95, and the smallest elevation of the 
sun is 12°. The utmost reliance may be placed on 
the zeal of our American brethren for observing the 
ino'ress. As oTcat facility exists for determinino; the 
absolute longitude of any place within the range of 
American telegraphs (Harvard having been accurately 
referred to Greenwich), it is unnecessary to look 
further. Otherwise it might be remarked that Ber- 
muda, Jamaica, and the West Indian Islands, and both 
sides of Central America, are excellent stations, but 
requiring determinations of longitude.' 



170 TRANSITS OF VENUS. 

VII. — ' Stations for observing the Egress as accelerated 
by Parallax^ — that is, Stations near E {^Plate III.), 
on the Illuminated side of CT>, but not too near C D. 
See note, p, 163. 

^ All the American stations mentioned in the last 
paragraph, from Halifax to Xew Orleans, and Ber- 
muda and the West Indian Islands, are well situated 
for this observation, the factors being near 0*85, and 
the sun's altitude varying from 4° at Halifax to 32° at 
Kew Orleans and Jamaica. The coast of South 
America also is favourable, from its union with the 
isthmus to the harbour of Rio de Janeiro. It is 
believed that efforts have been made for exact deter- 
mination, in a nautical sense, of the longitude of Kio ; 
it may now be desirable to give to that longitude the 
utmost accuracy.' 

YIII. — ' Stations for observing the Egress as retarded 
by Parallax'' — that is, Stations near E^ {Plate VII,), 
on the Illuminated side of C^ D^, but not too near C^ D^ 
See note, />. 163. 

^ Omitting for the present the Southern Continent, 
this observation will be amply secured by the obser- 
vatories of Sydney and Melbourne, where the factor 
is 0-96, and the sun's elevation 12° to 14°. If, how- 
ever, the longitudes of the Xew Zealand stations can 
be ascertained, they, with factor 0*8 and sun's eleva- 
tion 32°, will form a valuable addition.' 



THE COMIXG TBAXSITS. I/I 

Skcoxd, by the Method of Interval be- 
tween Ingress and Egress. 

' On compariDg Plates VI. and VII., it will be seen 
that the Xorth American localities supply, in a manner 
Avliich leaves nothing to be desired^ the demand for 
stations^ at which the ingress is retarded and the 
egress accelerated^ or the whole interval is diminished^ 
by parallax. 

' AVith these^ it is necessary to combine one or 
more stations^ at which the ingress is accelerated and 
the egress retarded, or the whole interval is increased, 
by parallax. On examining' Plates VI. and VII. j, ^it 
will be seen that the only possible method of respond- 
ing to this demand is by the selection of stations on 
the Antarctic Continent^ in which the observation will 
be made when the sun is nearlv below the Pole. 

' In so far as the coast of the Antarctic Continent 
follows nearly a parallel of latitude, the best position 
for a station is at 7^ east longitude. The factors 
would be, for ingress and egress, about 0'9o and 0*68. 
The sun would be, at each station^ about three hours 
from the sub-polar meridian. But its elevation above 
tiie horizon would scarcely exceed 4^^ and any altera- 
tion of the longitude^ with the view of increasing the 
elevation at one phenomenon^ would diminish it at the 
other. 

^Advantage may^ however^ be taken of the deep 
southern inlet discovered by Sir James Ross, to the 
western side of wliich is o;iven the name of South 



172 TRAXSITS OF VEXUS. 

Victoria. If a station cai] be establlshecl In latitude 
exceeding 72° S., it will be preferable^ for observation 
of ingress^ to the station in 7^ longitude^ and if the 
expedition could be pushed on to an observing place 
in the neighbourhood of Mounts Erebus and Terror, 
that position would be greatly preferable. For ob- 
servation of egress^ it is manifestly far superior ; the 
sun's altitude being about 27°. The factors for the 
two observations are respectively about 0*78 and 
0-58. 

' The decision on the choice to be made between 
these two stations, and the judgment on the facility, 
or even the possibility, of using either of them, must 
rest with persons who have had some familiarity with 
polar, and, if possible, with south polar voyages.' 

' In partial correction of some small inaccuracies in 
these remarks, it may be observed that — 

' The ingress, as viewed from the earth's centre, is 
always a few minutes earlier, and the egress always a 
few minutes later, than is supposed in the maps.' 

' As affected by parallax, the phenomenon is always 
retarded with ascending sun and accelerated with 
descending sun.' 

' As referred to apparent solar time, the phenomena 
are slightly retarded.' 

' The only phenomena which are critically affected 
by these corrections are those' of Plates IV. and V., 
' and in both the circumstances of solar elevation are 
rendered more favourable.' 



THE COMIXG THAXSITS. 173 

^ There may be a cause of uncertainty in the 
observation-elements on ^vhieh M. Le Verrier's tables 
of Venus are founded,, arishig from the unsatisfactory 
form in ^dnch the observations of the phmet were 
recorded in Bradley's time. At a critical inferior 
coniunction. when Venus was apparently a very large 
body, very deeply hollowed, it is impossible to say 
vrhether the limb was observed or whether an attempt 
was made to observe the centre. In my reductions of 
tlie planetary observations I inclined to the former 
idea. Subsequently M. Le Verrier adopted the latter. 
The tables are. at this time, very accurate, and it may 
prove that M. Le Verrier's interpretation was correct. 
Any uncertainty, however, of this kind makes it 
desirable to avoid ol servations of the ingress or egress 
very near to the horizon.* 

This account of Sir G. Airy's treatment of the 
two transits would be incomplete without some de- 
scription of his views as to the occupation of Antarctic 
stations, or without an account of the opinions ad- 
vanced in support of his views by authorities whom he 
had invited to attend the meeting of the Astronomical 
Society before which the above programme was 
advanced. 

In lSo7 the Astronomer Royal's remarks were 
thus reported (*' Monthly Xotices ' for May 185 7. p. 
216) : ■ The southern tract is a part of the Antarctic 
land discovered by Lieut. AVilkes. of the United 
States navy.^ included between Sabrina Land and 
^ This Antarclio ' land " had, however, been sailed ov-r bv Eoss ten 



174 TRANSITS OF VENUS. 

Repulse Bay. The Astronomer Royal is informed by 
General Sabine that December 6 is rather early in 
the season for a visit to this land^ but probably not 
too early^ more especially as firm ice will be quite as 
good for these observations as dry land. . . . It would 
be extremely desirable that the country should be 
reconnoitred some years before the transit.' (The 
whole passage should be studied^ but space will not 
permit me to quote any considerable portion of the 
passages I refer to here.) Again, in the same Report 
(p. 221): ^ The Astronomer Royal argues that the 
future astronomical public will not be satisfied unless 
all practical use ' (probably a mis-report for ^ prac- 
ticable use ') ^is made of the transits of Venus in 1874 
and 1882, and that for these the determination of some 
distant longitudes, and a reconnaissance of Wilkes's 
Land, must be effected within a few years.' 

The next remarks of the Astronomer Royal on 
this subject appeared in the ' Monthly Xotices ' for 
June 1864, pp. 173-177. In this paper^ after con- 
sidering the circumstances of the transit of 1882 
(leaving that of 1874 unmentioned), he proceeds to 
say : ' On the whole, I think it very desirable that a 
reconnaissance should be made of the points under 
consideration, and that it should not be long deferred. 
The first locality to be examined is that in 7^ east 
longitude, between Sabrina Land and Repulse Bay : 
and the points to be ascertained are — (1) whether the 

years before ; and in the later discussion of the subject Sabrina Land 
was substituted for Wilkes's supposed continent 



THE COMIXG TRANSITS, 1 75 

coast is accessible in December 6 : (2) whether a 
latitude of 65^ can be reached ; (3) ^vhether the snn 
can be observed ' (under certain conditions Ayhich 
affect the problem unfavourably in 1882^ but have no 
existence in 1874). ' Should the answer to the first 
or third questions be negative, then it would be proper 
to examine other portions of the South Continent, say 
in longitude not very different from 4^ west, but with 
no particular restriction except that of gaining the 
highest possible south latitude.' 

The next reference to the subject appeared in the 
' Monthly Notices^ for May I860, pp. 201-203. The 
paper bears the title, ' Letter from the Astronomer 
Royal to Sir R. I. Murchison, K.C.B., President of 
the Royal Geographical Society.' It runs thus : — 

' I have learned, through the public papers, the 
tenor of late discussions at the Royal Geographical 
Society in reference to a proposal for an expedition 
towards the ^'orth Pole. I gather from these that 
the object proposed, as bearing on science, is not so 
much specific as general : that there is no single point 
of very great importance to be obtained^ but a number 
of co-ordinate objects whose aggregate would be valu- 
able. And I conclude that the field is still open for 
another projDOsal, which would give opportunity for 
the determination of various results, corresponding in 
kind and in importance to those of the proposed 
Northern Expedition, though in a different locality, 
and would also give information on a point of great 
importance to astronomy^ which must be sought within 



^^6 TI^AXSITS OF VEXUS, 

a few years^ and which it is desirable to obtain as early 
as possible. 

^ In the year 1882, on December 6, a transit of 
Venus over the sun's disc will occur ; the most favour- 
able of all phenomena for solution of the noble problem 
of determining the sun's distance from the earth, 
provided that proper stations for the observation can 
be found. (It will be remembered that it was for 
the same purpose that the most celebrated of all the 
British scientific expeditions, namely, that of Captain 
Cook to Otaheite in 1769, was undertaken. The 
British part of the enterprise was perfectly successful ; 
but there have always been doubts of the accuracy 
of the corresponding observations in Lapland, which 
render a repetition of the observation very desirable.) 
In the ^' Monthly Notices of the Royal Astronomical 
Society " for June 10, 1864, I have very carefully 
discussed the circumstances of the comino; transit, in 
reference to the selection of observation-stations. For 
the northern stations there will be no difficulty ; they 
will be on the Atlantic seaboard of North America, or 
at Bermuda ; all very favourable and very accessible. 
For the southern stations the selection is not so easy ; 
the observation must be made on the Antarctic Con- 
tinent ; if proper localities can be found there, and if 
the circumstances of weather, &c., are favourable, the 
determination will be excellent ; if those favourable 
circumstances do not hold, no use whatever can be 
made of the transit.' 

Then follow certain sentences from the cited 



THE C03IiyG TEAXSITS. 1 7/ 

^ Monthly Xotices/ bearing on the selection of southern 
stations^ and including the passages which I have 
quoted above. The Astronomer Royal proceeds as 
follows : — 

' The astronomical object of a southern expedition 
is, I trust, sufficiently explained in the sentences which 
I have quoted. In the event of such an expedition 
being undertaken, the precise determinations which I 
have indicated as bearing on the astronomical question 
mnst (from the nature of the case) take precedence 
of all others. But there would be no difficulty in 
combining T\ith them any other inquiries, of geography, 
geology, hydrography, magnetism, meteorology, natural 
History, or any other subject for which the localities 
e suitable. 
^ And I have now to request that you will have 
the kindness to communicate these remarks to the 
Royal Geographical Society, and to take the sense of 
the Society on the question, whether it is not desirable, 
if other scientific bodies should co-operate, that a 
representation be made by the Royal Geographical 
Society to Her Majesty's Government on the advan- 
ta^re of makino; such a reconnaissance of the Southern 
Continent as I have proposed ; primarily in the interest 
of astronomy (referring to my official responsibility 
for the importance of the examination at this special 
time) ; but conjointly with that, in the interests, per- 
haps ultimately more important, of geography and 
other sciences usually promoted by tiie Royal Geo- 
graphical Society.' 

N 



178 TRANSITS OF VEKUS. 

In December 1868^ notwithstanding the relatively 
unfavourable circumstances for applying this (Halley's) 
method to the transit of 1882, and the very favourable 
conditions under Avhich Delisle's method can then be 
applied, the Astronomer Royal urged that only three 
stations should be occupied for Delisle's method in 
that year, the instruments of the five 1874 expeditions, 
' thus set free from two stations,' being required at an 
observing station on the Southern Continent. He had 
now so far changed his mind as to the method of 
dealing with Antarctic difficulties, as to speak in the 
following terms : ^ The choice of station being made,' 
he said, ' I would not recommend any reconnaissance, 
but I would propose that an expedition should go 
direct to the selected point in good time for the obser- 
vation of the phenomenon. The season is early for 
South Polar expeditions, and any difficulties produced 
by ice would probably diminish every day. A station 
being gained, all that is necessary in the way of sub- 
sidiary observation is a few days' observation to give 
clock-rate ; then the clock times of the two phenomena 
will furnish all that is required. The first action to 
be undertaken by the Grovernment,' he proceeds (and 
I invite special attention to the point), ^ is to procure 
the stock of instruments, and this ought to be done 
vrithout delay. An observing plant like that ' (de- 
scribed in the earlier part of the same paper ) ^ is not 
to be obtained in haste, and the proposed expedition 
might be entirely crippled by a small negligence 
on tins point. The equipment of ships and the 



THE COMIXG TRAXSITS. 1 79 

selection of officers would probably require much less 
time.' 

It appeared to the naval authorities who followed 
the Astronomer Royal in addressing the meetings that 
the more certain course for achieving the desired 
result would consist in the preparation of an expedition 
to winter in Possession Island. I quote the following 
passages as bearing specially on the feasibility of such 
an expedition : — 

Admiral (then Captain) Richards^ Hydrographer to 
the Admiralty, said : ' My own opinion, looking to the 
uncertainty of finding a wintering station for a ship, is 
that landing a party on Possession Island,' or one of 
the islands farther south, ^ would be the most feasible 
course, and there would be little doubt of the facility of 
reaching one or other of these islands with a suitable 
steam- vessel, making Tasmania or Xew Zealand the 
base of operations. Doubtless a year passed in this 
region would be most profitably employed in adding to 
our knowledge of magnetism, and various other branches 
of physical science.' 

Admiral Ommanney said, {?iter alia : ' I fully con- 
cur in all that has fallen from the Hydrographer to the 
Navy, and hope ere long to hear that operations are 
making for sending out to explore the Antarctic 
Seas.' 

Commander J. A. Davis, who had accompanied 
Sir James Ross in that most gallant expedition during 
which Victoria Land was discovered, and who had 
himself landed at Possession Island, said that ^ he 

N 2 



l80 TRAXSITS OF VEXUS. 

believed there would be no difficulty whatever in again 
effecting a landing in the same place.' ' AVith regard 
to the period of the season at which the transit took 
place^ it was to be remembered that the 6th of 
December was so early that no ships had ever reached 
the Antarctic Circle by that date ; and as it would 
be necessary to arrange the instruments^ &c. prepara- 
tory to the observation^ he might say that the ships 
ought to be on the spot at least a month before. This 
would be the 6th of Xovember^ a date altogether out 
of the question ; and as the ships could not winter in 
the Souths the party would necessarily have to land 
the year before ; but with good tents he had no doubt 
they could pass the winter very comfortably ' (this, of 
course, and what follows, will not be taken strictly 
au pied de la lettre) : ' they would have a pleasant 
prospect before them and plenty of penguins to live on. 
In comparison with Kerguel en Island and the Crozets,' 
he proceded, ^ the chances of observing the transit — 
meteorologically speaking — would be greatly in favour 
of South Victoria.' 

Captain Toynbee also expressed an opinion strongly 
adverse to the meteorological chances at Prince 
Edward's Islands, the Crozets, and Kerguelen Land, 
since their neighbourhood is, he said, ' so far as my 
experience goes, subject to a great deal of thick 
weather.' 

There were several points in the Astronomer 
Royal's communication to the Astronomical Society 
on this occasion which were calculated to attract 



THE COMIXG TBAXSITS. l8l 

the attention of those ^vho had followed his former pro- 
ceedings in connection with the transits of 1874 and 
1882. Thus far he alone of all the leading astro- 
nomers had publicly dealt with the subject, and there 
was much in the tone of his preceding papers to sug- 
gest that in a sense he guaranteed a sufficient examina- 
tion of the conditions of the transit to enable astronomers 
generally^ not those of England alone^ to await his 
announcement of what the different scientific nations 
might be expected to do^ and to follow his instructions 
whensoever such announcement should be made. In 
the paper of December 1868 he still adopted tliis tone, 
while nevertheless it was apparent that he was not 
treating the subject in an exact manner. For instance, 
the statement in the very beginning of his paper that 
the method of duration had been sltoicn to ^ fail totally,' 
even if correct in itself— which subsequent examination 
showed not to be the case — was not in accordance with 
former papers, in which he had only expressed his 
opinion that in all likelihood it would not be advan- 
tageously applicable. Then secondly, the maps accom- 
panying the paper were of the roughest possible de- 
scription, insomuch that the shapes of the continents 
and oceans were barely recognisable : nor did these maps 
extend beyond the parts immediately adjacent to the 
points corresponding with I, i\ E, and E^ in Plates VI. 
and YII. ; so that if by any possibility (which seemed 
at that time, however, incredible) Halley's method 
should be available in 1874, the maps could not have 
shown the fact, though this was precisely the sort of 



1 82 TB Ay SITS OF VEX US. 

service for which alone maps could have anv real 
value. Thirdlv. the necessity for exact accuracv 
seemed so little to be suspected by Sir G. Airy, that 
the elements of the transit, given correctlv bv Hinft, 
were not even congruously employed, the times of 
ingress and egress being these corresponding to b. V of 
Plate XI.. while the positio?is were those corresponding: 
to external contact, points which in reality are farther 
away from b and b' than are c and c respectively. 

Whether these circumstances operated with Puiseux, 
Hansen. Peters, and others who about this time began 
to inquire into the condition- of the two transits ' and 
sooner or later published correct results),! do not know ; 
but. for my own part^ I was led to deal with the subject 
by the manifest signs of incompleteness in Sir G. Airy's 
paper. It appeared to me that there was room for a 
rediscussion of the whole problem, even thou2"h. as I 
fully expected, the general views advanced in that 
paper should prove to be altogether correct. 

But I found that in many important respects, 
and in one or two of critical importance, those state- 
ments were incorrect. In particular I found that 
Halley's method, instead of failing totally in IS 74, 
could be applied under highly favourable conditions, 
even without attempting to find stations on the Antarctic 
continent. On the other hand, this method, instead of 
being applicable in 1S82. fails totally for that transit, 
even though the selected Antarctic stations could be 
reached. But this was not all. The points corre- 
sponding to i_. i'. E,, e' of Plate YL. on the right 



THE COMIXG TEAS SITS, 1 83 

placing of which depends the determination of the true 
relative value of Delislean stations^ Tvere incorrectly 
placed in Sir Gr. Airy's maps by two hundred and eighfjj 
miles, eight hundred miles^. seven hundred miles, and 
two hundred and twenty miles respectively ! And per- 
haps even more remarkable than this strange incor- 
rectness, was the complete omission (from among the 
stations for obser^'ing retarded egress; of Xorth Indian 
stations specially falling ^4thin the range of British 
duties in the matter. This was due to the roughness 
of the maps, for the map illustrating this phase, 
presenting the region near E in Plate YI.^ did not 
show Xorth India at alL the title of the map occupying 
the space (10, in Plate XIII.) where Xorth Indian 
towns should have been shown. 

In March 1869 I published a paper containing the 
first stages of a rediscussion of the problem, precisely 
as worked out in my note-book, from the beginning, 
when I had no suspicion that any important correction 
would have to be made, to the stage when I first 
recognised that Halley's method would be more suit- 
able in 18 74 than in 1882. In February 1869 I had 
communicated this fact to the Astronomer Koyah from 
whom I received a reply which lies before me as I 
write, beginning, • I think it very likely , (the italics are 
mine) ' that the difterence of durations in the transit 
of 1874 may he greater than in 1882 ; ' clearly showing 
that even at that comparatively late day the Astronomer 
Koyal was not more certain about the conditions of the 
transit of 1882 than he had been twelve vears earlier 



1 84 TRANSITS OF VENUS. 

when he said that the difference of durations in the 
transit of 1874 would 'probably not be half of that in 
1882.' So that I confess it Avas with some surprise 
that I read a letter to the Astronomical Society (almost 
contemporaneous with the one addressed to myself), in 
Avhich he stated that in 1857 he had ^ fully considered' 
the application of Halley's method to the transit of 
1874. An inference in 1857 that the difference of 
durations in 1874 iconld probably not be half that in 
1882^ and a belief in February 1869 that the difference 
in 1874 may probably be greater than in 1882^ did not 
seem to me then, and does not seem to me now, to 
correspond with a ' full consideration ' of the method 
depending on this difference of duration. The letter 
to the Astronomical Society just referred to is note- 
worthy, however, as mentioning a criterion which at 
that time Sir G. Airy adopted in comparing Delisle's 
and Halley's methods : ^ I hope,' he says, ' the probable 
error of g-eometrical long^itude loill not be more than 
one-half of the probable error of ingress or egress.' ^ 

' Subsequently when it became necessary to make out that Delisle's 
method was nearly equal in value to Halley's, Sir G. Airy and Mr. Stone 
insisted that the probable error of geographical longitude would be less 
than one fourth of the probable error of an observation of contact. This 
was done by reducing the estimate of the probable error in longitude de- 
terminations. All the time, the probable error of an observation of ingress 
or egress was inferred from the results of 1769, without any account being 
taken of the probable diminution of this error in consequence of the in- 
quiries and experiments which have been made into its cause and nature. 
This is idle. If those inquiri es and experiments are valueless, why should 
so much be said of them in the G-reenwich Reports ? If they are valu- 
able, as we all hope and believe, why is the error which they are intended 
to reduce, treated as though it would probably be as great as ever ? 



THE COMING TRANSITS. 1 85 

Having now ascertained that tlie subject had not as 
yet been thoroughly dealt with, I resumed the investi- 
gation, and in May 1869 I submitted to the Astrono- 
mical Society a paper accompanied by six projections 
(from two of which Plates XVIL and XYIII. have 
been reduced by photolithography) illustrating the 
transit of 1874. This paper was published in the June 
number of the ' Monthly Notices.' I had by this time, 
to my regret, learned that my inquiries into the 
subject were distasteful to the Astronomer Royal, and 
therefore I avoided all mention even of his name in 
this paper ; and where it was necessary to call due at- 
tention to the changed values of the various stations, I 
presented these in a tabular form, — Airy's values under 
head a, those of Puiseux under head B, and my own, 
which closely accorded in the main with those of 
Puiseux, under head c. 

As some have supposed that I wished solely to sub- 
stitute Halley's method for Delisle's (a change which 
would have been of little value), I deem it well to 
quote here from my paper of May 1869, the following 
summary of the conclusions therein demonstrated : — 

1. ^ The application of Delists method of absolute 
time differences. The relative as well as the absolute 
values of many stations are affected. Some which 
had hitherto appeared unsuitable are found to be un- 
objectionable. Others which seemed good appear unfit. 
In other cases the relative values of two stations are 
so affected that the results of a comparison between 
them are directly reversed. Lastly, many stations 



1 86 TRANSITS OF VENUS. 

not hitherto thought of in connection with the transit 
are found to be well suited for the application of Delisle's 
method. 

2. ' The comparison hetioeen Delisle's and Halley'^s 
methods. Halley's method ' (estimated by Sir G. 
Airy's own test) ' is found not merely to be applicable 
with advantage, which is all that can be said of it when 
central passages are considered, but to be superior to 
Delisle's — slightly, when reference is made only to 
such stations as had been hitherto dealt with, notice- 
ably when Antarctic stations are made use of. 

3. ^ The comparison between the transits of 1874 
and 1882 loith reference to Halley s method. This 
comparison shows that Halley's methodmay be applied 
much more advantageously to the transit of 1874 than 
to that of 1882. '1 

The tables (which are given in abstract at the end 
of this volume) were followed by these remarks : — 

' It will be seen, on a comparison of tables A, B, 
and C, that the effects of the change of phase are in 
some cases important. The coefficients of parallax are 
affected in several instances by more than 0*1 and in 
two cases by 0*22. In the cases of Crozet Island 
(Table II.) and Chatham Island (Table III.) solar 
elevations are so improved, that these stations, which 
would have to be rejected if central passage were con- 

* Chapter IV. presents in pp. 128 et seq. an abstract of the reason- 
ing by which the apphcability of Halley's method in 1874 was demon- 
strated, and also indicates the places where the method can be most 
suitably applied. But the tables at the end of the book should be con- 
sulted, especially Table V. 



TRB COMIXG TRAXSITS. 1 8/ 

sidered^ are shown to be well suited for the observation 
of internal contacts. The diminution of all the co- 
efficients in Table III., through the change of phase^ 
■ has an importaut influence on the value of Delisle's 
method, so far as egress observations are concerned. 
It is important to notice, also, that under the heads C 
in Tables III. and lY. many stations not hitherto 
recognised as available are included among the best 
places for observing egress. The Indian stations in 
Table I Y. seem too valuable to be neglected.^ Pesha- 
wur is better even than Alexandria: Delhi is not 
inferior to the latter station (when solar elevation is 
considered as well as coefficient of parallax). Bombay, 
Calcutta, and Madras are also excellent. It may be 
noticed also that Bombay and Madras, which, when 
considered with reference to central passage, had 
seemed suitable places for the observation of retarded 
ingress, are found to have so poor a coefficient of 
parallax when reference is made to internal contacts, 
that it would seem useless to observe ingress there (so 
far at least as the application of Delisle's method is 
concerned). 

' Of course, it will be impracticable for this country 
to send observers to more than a certain number of 
stations. But it is not unlikely that besides Russia, 
France, and England (the only countries specially 
concerned in the transit of 1874), other nations may 

1 Several times during the past year the mistake has been made of 
stating that I originally advocated Xorth Indian stations for applying 
the photographic method. The above passage, written before this method 

had been thought of, contams mv first reference to those stations. 



1 88 TRANSITS OF VENUS. 

care to take part in the solution of the noble problem 
of determining the sun's distance ; and thus it seems 
advisable that all the stations where there will be any 
chance of obtaining useful observations, should be , 
tabulated as nearly as possible according to their rela- 
tive values.' 

A discussion followed in which an attempt was 
made to show that Delisle's method w^as equal in value 
to Halley's. Even if this could have been proved , it 
would have been little to the purpose, since the ques- 
tion was not whether Halley's method was more or 
less favourably applicable than Delisle's, but whether 
it was applicable at all. This discussion was carried 
on in public. A private correspondence arose out of 
a letter which I addressed to Sir Gr. Airy, assuring 
him that my sole wish was to assist in securing what 
every astronomer agreed was desirable — the best pos- 
sible utilisation of the opportunities available in 1874 
and 1882. Sir G. Airy wrote me a letter, forwarding 
a copy to Admiral Manners, then President of the 
Astronomical Society, in which he complained that his 
paper of December 1868 had been treated as though 
it claimed to be an exact discussion of the conditions, 
due allowance not beino; naade for his own statement 
that it was but a preliminary and comparatively rough 
investigation of the problem. This led me to believe 
(mistakenly, as afterwards appeared) that I had taken 
up the subject too hastily; for Sir Gr. Airy seemed 
not merely to promise a thorough analysis of the whole 
subject, but to imply that this was what had been 



THE COMIXG TRANSITS, 1 89 

intended all along, the suggestions made in December 
1868 being merely provisional^ and the actual arrange- 
ments to be proposed to Government depending on the 
promised thorough investigation. 

Nothing could have been more satisfactory than 
the course thus indicated ; and^ accordingly^ from that 
time (the summer of 1869) until the summer of 1872^ 
I addressed no communication whatever on the subject 
of the controversy^^ either to Sir G. Airy personally 
or to the Astronomical Society. Nothing, however, 
was done in this interval except to carry out the 
arrangements proposed in 1868. Accordingly, in 
1872 I Avrote to Sir G. Airy, recalling his attention 
to the promised investigation of the subject. I then 
learned for the first time that the old arrangements 
were still adhered to. On this, I made such protest 
as a student of astronomy, independent of official 
trammels, might properly (in my judgment then a:id 
now) address to the official astronomer to whom the 
charge of the matter had been left in accordance with 
ancient custom. 

After this protest I allowed yet half a year more 
to elapse, and then^ nothing having been done, it 
seemed time to take more earnest measures.^ 

* A paper of mine appeared in ttie ' 3Iontlily Notices' for January 
1870, in which the application of photography to the observation of the 
transit was dealt with ; but this paper bore no reference to the ques- 
tions which had been raised by me in 1869. 

2 In the interval events had taken place within the Astronomical 
Society to which I see Sir Edmund Beckett has thought it desirable to re- 
fer in the latest edition of his ' Astronomy without Mathematics.' Those 
events had no real importance, howeyer, except for the animus shown. 



IQO TRANSITS OF VENVS. 

I accordingly resumed the discussion in the ^ Spec- 
tator ' for February 8. By a singular coincidence a 
powerful paper appeared in the ^ Times ' of February 
13 supporting the views Avhich I had advanced. This 
paper was commonly^ and I believe correctly, attri- 
buted to Sir Edmund Beckett. (In his ^ Astronomy 
without Mathematics' he mentions the rumovir without 
contradicting it.) And many believed that the co- 
incidence was not accidental — that is, that the nearly 
simultaneous appearance of the two papers had been 
planned beforehand. But this w^as not the case. 
Neither had Sir E. Beckett any prior knowledge of 
my intention, nor had 1 of his. 

What followed strikingly illustrated at once the 
power of the press and the unwillingness of the official 
mind to move from a position once taken up. Aware 
of the latter peculiarity, I thought it desirable to bring 
my proposals forw^ard in such a way that some point 
might be flatly refused, in order that essential matters 
might be yielded. It w^as not difficult to effect this. 
There w^as very little prospect at that late date that 
Antarctic stations would be occupied for the transit of 
1874. Enderby Land and Possession Island, near 
South Victoria Land, were, geometrically, among the 
best southern stations for observing the transit ; and 
if all had been trustworthy that w^as said of the last- 
named station by Admiralty officers in December 1868, 
this station w^ould have been not only geometrically 
excellent but meteorologically preferable to most of 
the southern stations already provided for. It re- 



1 



THE COMING TRANSITS. 191 

quired, indeed, that a party should winter there ; and 
I had pointed out two years before, in ^ The Sun/ the 
fact (which Commodore Davis seemed to have for- 
gotten) that when Ross landed there in 1847, the 
sailors were quickly compelled to retire by the abomi- 
nable smell proceeding from the accumulations of 
guano. The proposal of an Antarctic station was 
therefore an excellent one to be refused, if, by allowing 
the official mind that luxury, concession might be 
obtained on other and more important points. 

]\Iatters befell as I anticipated as respects the 
refusal, though concessions were not at first made 
very willingly. ^ On a review of the whole case,' said 
the Astronomer Royal in his reply, ' I decline to 
recommend that an expedition be sent to any station 
on the Antarctic continent.' 

Per contra^ no concession was made except the 
admission that North India ought to be occupied by a 
photographic party (not as a Delislean and Halleyan 
station). The use of Halley's method was opposed 
absolutely, on the ground (i.) that the Russians would 
probably not occupy Nertschinsk, the station in Siberia 
(marked 6 in Plates XII. and XIII.) which I had 
specially recommended, (ii.)that Puiseux had probably 
abandoned his ideas respecting the use of Halley's 
method (which ideas, said Airy, ■' have not again 
been promulgated on the Continent '), and (iii.) that 
no other nations would care to provide for northern 
Halleyan stations. A few days later, ^Mr. Goschen, 
then Secretary of the Admiralty, said that even at 



192 TRANSITS OF VENUS. 

those stations already provided for, where, as I had 
shown, durations could be readily noted, they would 
indeed be noted, but little reliance would be placed on 
theml^ 

An unfortunate contretemps diminished the effect of 
this official immobility. Within a few days from Sir Gr. 
Airy's declaring his belief that other nations would 
not apply Halley's method — nay, that probably not even 
a solitary northern Halleyan station at Nertschinsk 
would be occupied — came news that Russia proposed 
to occupy not only Nertschinsk^ hut ten other Halleyan 
stations in Siberia ; that America proposed to occupy 
three other northern Halleyan stations ^ Germany 
two others ; and before long it was announced that 
France would occupy two other northern Halleyan 
stations. 

But it was still possible that these energetic pro- 
ceedings by other nations might be rendered useless 
by shortcomings on our part; for as yet no ade- 
quate provision had been made for southern Halleyan 
stations, and it w^as manifest that other nations were 
looking to England to take a large share in this part of 
the work. Eighteen northern Halleyan stations were 
provided for, and as yet only one first-class southern 
Halleyan station, Kerguelen's Land, — and that origi- 



* Sir George Airy soon after wrote to me that there bad been some 
misunderstanding here. I should concei\"e on the whole that there had 
been. It may perhaps be easily understood that Mr. Goschen, who, 
of course, had no technical familiarity w\\h. the subject, might have 
misapprehended some statement addressed to him by Sir G. Airy. 



THE COMING TRANSITS. 1 93 

nally named without the least idea that it was a 
Halleyan station at all. 

The time had come for very plain speaking. Be 
it noted that if Delisle's method succeeded at each of 
the selected stations, then the transit would yield very 
good results ; but even then not so good as though 
Halley's method were extensively applied in addition. 
For every method successfully applied, and indeed 
every observation, reduces the probable error in the 
final result. But there was at this stao;e a risk that 
the operations would fail altogether.^ If, as Avas and 

^ Very strangely, what I said in May and June 1873, about a great 
risk of failure, has been regarded as altogether inconsistent ^dth what 
I have said during the present year about a great chance of success. Mr. 
Christie, (described in the 'Greenwich Keports' as 'the Astronomer 
Royal's confidential representative,') gravely took me to task in the 
'Academy 'for this alleged inconsistency; and even in an exceedingly 
fair-spirited review in the ' London Quarterly,' my fears in 1873 are thus 
referred to : — ' This we think is where Mr. Proctor has erred ; for he 
subsequently expresses at least comparative satisfaction with the final 
arrangements.' I will now give the very words in which in June 1873 
I described the risk of failure in ' Eraser's Magazine ' : — ' Let the fol- 
lowing startling facts be noted in conclusion-. If there is bad weather 
either in the Sandwich Lsles on one side, or at the Mauritius group and 
Kerguelen Island on the other, Delisle's method applied to the beginning 
of the transit will fail totally. If there is bad weather either in the 
New Zealand Islands, or at the opposite northern stations, Delisle's 
method applied to the end of the transit will fail totally. There would 
remain, then, only the chances depending on the three methods which 
require that the whole transit should be seen. For these methods 
ample provision has been made in the northern hemisphere, by Eussia, 
Germany, and America ; so much so that England's neglect as regards 
her North Indian stations becomes of relatively small importance. But, 
in the southern hemisphere, Kerguelen Island is the only really well- 
placed station to be occupied for applying these methods, and at 
Kerguelen Island fine weather occurs on about one day in ten. There 
remain the Macdonald Islands, suggested (only) for occupation by 

O 



194 TBAKSITS OF VEXUS, 

is possible, Delisle's method were to be frustrated by bad 
weather at the Sandwich Islands or at Kerguelen Island 
and neighbouring stations, then ingress observations 
would fail. If egress observations were to be frus- 
trated by bad weather at Xew Zealand and neighbour- 

Germanv. but unlikely to be occupied except by a specially nautical 
nation. Yet tlie whole space between Kerguelen Island, Enderby Land, 
Possession Island, and Auckland Island, is suitable for the three methods 
(and also, be it noted as important, for Delisle's method). There are 
several islands scattered over this region, and probably many others 
which have not yet been discovered. It is most unfortunate that nothing 
has been done, during the four years which have passed since I noted 
these facts, to make reconnaissances over the whole of this region ; but 
surely it will be even more unfortunate if no station is occupied in it. 
Of the duty of Great Britain in this matter I have spoken earnestly, 
because I feel warmly. Viewing the matter as an Englishman, I may 
say that I should feel concerned if this duty, neglected thus far by us, 
should be undertaken by America, the country to which, next after us, 
the duty belongs. But viewing the matter as a student of science, my 
great wish is to see due advantage taken of the great opportunitv af- 
forded by the approaching transit, without specially caring whether 
this country or another obtain more honour in accomplishing the task.' 
Now if this warning be viewed in connection with the fact that instead 
of one first-class southern Hallej'an station there will now be four, be- 
sides extra stations on Kerguelen Island (forty or fifty miles apart) and 
many new second-class stations, I think satisfaction now will be found to 
be altogether consistent with dissatisfaction in May and June 1873. For 
my own part, however, I am satisfied, rather as a student of science than 
as an Englishman, for of all the four really unpleasant stations in the 
Southern Seas, England occupies the one which is most conveniently 
accessible. But I was not careful to dwell on this point, nor should 
I do so now, were I not compelled by a charge of inconsistency, as 
singular as the dissatisfaction ^ith which my satisfaction has been 
viewed in certain quarters. If I am asked to admit that my suggestions 
were very slowly adopted, and that even now we ought not to be 
altogetlier satisfied, I am ready to do so. General satisfaction at the 
removal of the great risk of failure is not inconsistent with the feeling 
that much more might have been done by England, and that since 
America must occupy the first place in the transit of 1882, we need not 
have suffered her to be so completely ahead of us in the transit of 1874. 



THE COMIXG TRAXSITS. 1 95 

ing stations^ or at the opposite region^ then egress obser- 
vations would fail. In either case very imperfect results 
would be attained; but if both events were to happen, 
then no result at all would be achieved. Now there 
were eighteen northern Halleyan stations admirably 
suited to supply a third chance of success by Halley's 
method if they were but properly balanced in the 
southern hemisphere^ but otherwise valueless. For 
although^ besides being Halleyan, they were also ex- 
cellent as subsidiary Delislean stations (each having a 
double chance, because either the beoinnins^ or the 
end would serve for that method), yet the multipli- 
cation of northern Delislean stations could not remove 
the chances of failure on account of the fewness of 
southern stations. In either respect, whether to 
balance the northern Halleyan stations as such, or to 
o'ive new Delislean chances, nothing; was at that time 
promised. Apart from all question of the choice or 
methods, there was no suitable provision for southern 
observation. Kerguelen's Land was the only first- 
class Halleyan southern station yet provided for, and 
none of the other southern stations could be regarded 
as high even in the second class. These others — 
Canterbury Island, Auckland Island, Mauritius, and 
Rodriguez, stood fairly well in the second class, and 
that was all that could be said. The only good station, 
Kerguelen's Land, was one at which all the meteoro- 
logists had said that, bad weather was far more pro- 
bable than fair weather. I had already pointed out, 
as geometrically suitable, Kemp Island, Crozet Island, 



196 TRANSITS OF VENUS. 

Macdonald Island^ the group of islands of which 
Campbell Island is the chief, St. Paul's Island, and 
several others of less value, yet well worth occupying 
if geographically suitable. But Admiral Richards, 
without mentioning these islands by name, had in the 
^Times' described me as recommending the occupation 
of places which were 'little better than geographical 
myths.' 

It began to appear as though, after all, nothing 
would be effected until too late, so that perhaps some 
time about the year 1877 or 1878 astronomers would 
be lamenting that the favourable opportunities presented 
by the transit of 1874 had not been properly utilised. 

But at this critical stage a new force appeared 
on the field, and compelled the Admiralty to retreat 
from the position they had so bravely defended. The 
Board of Visitors at Greenwich met on June 7, 1873, 
and it w^as there proposed, by Professor Adams, and 
carried unanimously, that Professor Cayley, who in 
his capacity as President of the Astronomical Society 
was Chairman of the Board, should apply to Govern- 
ment ' for the means of organising parties of observers 
in the Southern Seas, with the view of finding addi- 
tional localities in the sub-Antarctic regions for observ- 
ing durations ' — that is, for applying Halley's method. 
Of course, no one expected that this application 
would be acceded to in full. The course pursued by 
Government had thus far been the usual one in cases 
wnere it is feared that a change of plan may be con- 
strued into an admission of error. Sir G. Airy had 



THE COMING TRAXSITS, 197 

been asked to inform the Secretary to the Admiralty 
whether the Astronomer Royal's arrangements were 
well-considered ; and Sir George Airy had replied in- 
dicating his entire approval of the Astronomer Royal's 
arrangements. Admiral Richards had expressed the 
opinion that the Hydrographer to the Admiralty was 
quite right in regarding as ^ geographical myths ' in 1873 
places which in 1868 Admiral Richards had thought 
^easily accessible.' ' Moreover ' the suggestions made by 
Sir G. Airy and Admiral Richards in 1868 ^had not 
been brought before the Admiralty in an official form ' — 
that is, were not the suo^o-estions of the Astronomer 
Royal and the Hydrographer to the Admiralty. It is 
perhaps open to question Avhether this way of in- 
quiring into the matter was the one best calculated to 
elicit just opinions or to lead to satisfactory results. 

Yet the Government could not remain altogether 
Idle, when the leading astronomers of England re- 
quested that something might be done (for even Sir 
George Airy, in yet a third character, supported Prof. 
Adams' proposal). Fortunately, the ' Challenger ' 
was vovao-ing; in the Southern Seas, and could be 
employed to reconnoitre Kerguelen Land (a part of 
her original programme), and to get a distant view of 
Macdonald Island. The result, presented in combina- 
tion with a storm or so, has been held to establish con- 
clusively the inaccessibility of those ^ geographical 
myths,' which Cook, Ross, and other Antarctic 
voyagers (some of them still living) perversely insisted 
on visitino;. 



198 TRANSITS OF VUNUS. 

But other nations have not been deterred by 
the dangers and difficulties which unquestionably 
have to be encountered in voyages to sub- Antarctic 
stations. America, inquiring among sealing captains, 
found that the Crozet Islands could be occupied, 
and determined to send an observing party to that 
first-class Halleyan station, as well as to occupy 
second-rate Halleyan stations in Tasmania, New Zea- 
land, and Chatham Island. The French Government 
decided to occupy Campbell Island and St. Paul's 
Island (those inaccessible ^ geographical myths '), be- 
sides a second-rate southern station at Caledonia 
Island. Thus already the first-class Halleyan stations 
had been quadrupled in number, and the second- 
class largely strengthened. Germany and America 
both proposed to occupy Macdonald Island, if pos- 
sible, but found that this island (sometimes called 
Heard Island) really is almost, if not quite, inacces- 
sible, though an attempt will be made to land a party 
there. Our own country sends a second observing 
party to Kerguelen Island (to be stationed fifty miles 
from the other), with instructions to occupy Mac- 
donald Island, if possible.^ If not, there w^ill be four 
parties in different parts of Kerguelen Land ; and 
as the island is large, and the different parties will 
employ, besides Delisle's and Halley's method, two 
different modes of photographing the transit, we may 

^ So the chief of the two English Kerguelen parties informed me. 
What I learned when in America from IVIr. Chappell, the head of the 
sealing merchants in those seas, does not encourage me to beheve that 
the attempt will succeed. I hope it will be made^ however. 



THE COMING TEANSITS, ' 199 

consider that the Kerguelen stations will be equivalent 
to at least two separate chances of success. Adding 
the first-class Halleyan stations, Crozet, Campbell, 
and St. Paul, and the second-class stations, Bourbon, 
Rodriguez, Mauritius, Hobart Town, Melbourne, 
Sydney, &c., as well as the first-class Delislean 
stations in the South, and remembering that all the 
southern stations are good Delislean stations, w^hile 
several of the added Halleyan stations are doubly 
good Delislean stations because serving both for in- 
gress and for egress, it must be admitted that the risk 
of failure to which I pointed in May 1873 has been 
as completely removed as circumstances allowed. It 
would be no exaggeration to say that tlie chances of 
success have been quadrupled since then. 

I have omitted to mention (in fact, the change was 
made so quietly that I do not know where to place it) 
that the North Indian station Eoorkee, which had 
been first described as only to be used for photography, 
is now provided for as a Delislean and Halleyan station. 

About this time it was discovered : — 

First, that when Sir G. Airy said the method of 
durations fails totally in 1874, he meant Halley's 
method as it would have been used if the transit of 
1761 had been nearly central.^ Secondly, that from the 
beginning he always meant to apply Halley's method 
in 1874, wherever it could be applied.^ Thirdly,^ that 

* See 'Nature' for June 1874. Compare note, p. 162. 

2 See 'Naval Magazine' for October 1874. 

3 See 'Academy' for August 1874. 



200 TRAXSITS OF VFXUS. 

Halley's method is not realli/ to be applied by English 
observers^ since they are not instructed to observe the 
duration of transit, but to observe the time when transit 
begins and ends. 

Major a canamus. 



In the meantime, a new and most iuiportant 
auxiliary method of observing the transit — the photo- 
graphic method — which may hereafter, even if not in 
the case of this year's transit, become the most trust- 
worthy of all, had been suggested by Dr. De la Rue, — 
or rather, it may perhaps more fairly be said, that 
this method, first suggested by Faye, had been ex- 
hibited in a practicable form by De la Rue. 

In December 1868 Dr. De la Rue read a paper 
before the Astronomical Society containing the follow- 
ing remarks, inter alia : — 

^ The conditions which transits of Venus offer for 
the determination of the relative position of the sun's 
and planet's centres are more advantageous than those 
presented by solar eclipses, inasmuch that it is far 
more easy to measure directly the distances between 
the centre of the disc of the sun and that of the image 
of the planet upon it, than it is to measure the dis- 
tances between the peripheries of the sun and moon,* 
or the angular opening of the cusps ^ of the partially 
ecHpsed sun. And in transits of Venus any error of 
observation would not affect the final result nearly so 
much as in solar eclipses ; for example, in the transits 

' mil Trans., p. 383, Table I. ^ j^^ p, 55^ Table III. 



THE COMIX G TRAXSITS. 201 

of 1874 and 1882, an error of V^ in the measurement 
would, for the maximum displacement, give an error 
of only 0'^'185 in the deduced solar parallax, 

^ Moreover, it may be observed that in photo- 
graphic records it is by no means important to catch 
exactly the phases of contact, as two photographs 
obtained at a sufficient interval afford the means of 
calculatino; to a o;reat deo'ree of refinement, and of 
tracing, the path of the planet, which, for the condi- 
tions of the problem, may be considered to be a straight 
line between the two positions recorded. 

^ Xor is it in any way essential, as it is with eye- 
observations, that favourable conditions should exist 
for retarding the period of contact at one station and 
accelerating it at another, because the chords repre- 
senting the planet's path can be derived from photo- 
graphic records with as much accuracy under what 
would be considered unfavourable conditions as under 
favourable conditions for eye-observations, for the 
length of the chords need not be directly considered 
in determining the nearest approach of the sun's and 
planet's centres. 

' During the duration of the transit, it would be 
possible, in a clear state of the atmosphere, to obtain 
a series of photograjDhs at intervals of two or three 
minutes, and any or all of these would be available for 
comparison with the records obtained at all the stations 
selected. 

^ The epoch of each photographic record is deter- 
minable with the utmost accuracy: 1st, because the 



202 TRANSITS OF VENUS. 

time of exposure is not more than the ^^th or the y^th 
of a second ; and 2nd, because the instantaneous slide, 
as it flashes before the secondary lens, affords an 
audible signal ^ by striking against a stop a small 
fraction of a second after it has shut off the image of 
the sun. This interval might be determined by ex- 
periment and taken into account. 

' In the Kew Photoheliograph the solar disc would, 
at the epoch of the transit of 1874, have a semi- 
diameter of 1965*8-thousandths of an inch (a diameter 
of nearly four inches), Venus a semi- diameter of 63*33 
of these units, and the parallax of Venus referred to 
the sun would be represented by 47 'So of these units ; 
the maximum possible displacement being 95*7 units, 
or nearly jV^h of an inch. In 1882 the sun's semi- 
diameter would be 1964*9 imits; that of Venus 63*31 
units ; the parallax of Venus referred to the sun 
47*82 units; the maximum possible displacement 95*6 
units. 

' When the photographs have been secured, the 
measurements by means of the micrometer, which 
would have to be performed, consist in determinations 
of the sun's semi-diameter, in units of the arbitrary 
scale of thousandths of an inch, the angle of position 
of ' different positions of the centre of Venus, and the 
corresponding distances of her centre from the centre 
of the sun. ' The measurements by means of the 
micrometer described in the ^^Phil. Trans." 1862, pp. 
373-374, can be obtained to the 2-oVo"th of an inch 

^ Fhil. Trans., p. 364. 



THE COyJIXG TRAXSITS. 203 

(0^^*25)^ and the position angles to one or two seconds 
of arc. For each photograph measurements made at 
different times are remarkably accordant ; the greatest 
difference between the semi-diameter of the sun of the 
several eclipse pictures of 1860 was j-^-^ths of an inch^ 
or about 4^^*5 ; but^ on taking the mean of measure- 
ments of forty-five photographs by two different 
methods, the difference was only j^^ths, or about 
O'^*7o. I am inclined to believe that the distance 
could be ascertained to within V^ by means of a few 
pictures, and possibly to 0^^*25, if a sufficient number 
of photographs were obtained. 

' Fears have been expressed that the collodion, in 
drying, becomes distorted; experiments, however, in 
1860-61 have demonstrated that the shrinkage is only 
in the direction of the thickness. But as, in the case 
of the solar parallax, no refinement of correction ought 
to be neglected, it would be quite easy to ascertain 
once more whether any distortion does take place, by 
taking photographs on glass plates on which lines 
about a quarter of an inch distant had been previously 
etched; the collodion, which should be rendered 
purposely contaminated with particles in suspension, 
should be poured on the ruled sides to avoid parallax. 
After all the operations of photography, the film would 
have to be examined from the back, and the position 
of certain impurities with reference to the ruled lines 
noted whilst the collodion was wet, and after it had 
dried. 

' No difficulties exist in photographing a transit of 



204 TRANSITS OF VEXUS. 

Venus; the operations are quite the same as those 
practised daily at the Kew Observatory ; no strain on 
the nerves would occur, as in the anxiety consequent 
on the desire of rendering available every moment of 
the short duration of a solar eclipse. All the opera- 
tions could be conducted with that calm so essential 
for such a problem as the determination of the solar 
parallax, and I feel confidence in recommending that 
timely steps should be taken to secure photographic 
records of the transits of Venus in 1874 and 1882.' 

Three months later, Col. Tennant wrote a paper 
commenting on the practical details of Dr. De la 
Rue's plan, in the course of which he pointed out 
that ^if an observer at a separate telescope had a 
break circuit key he could at any moment photographi- 
cally record a phenomenon he saw and the instant of 
its occurrence. An assistant at the heliograph would 
be needed to replace the shutter and insert the dark 
slides, unless the observations are far apart. By using 
a repeating slide and combining the measurements on 
one plate, very valuable normal relations of the sun and 
planet would be found, and observations might be 
made during the ingress or egress (possibly, too, of the 
black drop) in considerable numbers. There is an 
advantage in this mode of observing the transit of 
Venus to which Dr. De la Rue has not alluded.^ If 

^ ' Dr. De la Eue has pointed out,' says Col. Tennant, ' the facility 
-^"itli -^-liieh the nearest approach can be got from the photographs at 
any one station, bnt if photographs be taken at two stations at a time 
when Yenus is in the plane which includes them both as well as the 

earth's centre, these will show the whole effect of parallax; and it is 



THE COMIXG TRAXSITS. 20 5 

accurate micrometrlcal observations can be made by 
means of photographic pictures^ then the range of suit- 
able stations can be greatly enlarged ; for any two 
stations, 140° or 150° apart, can have the observations 
combined by choosing a suitable time, and, of course, 
by means of equations of condition, the observations of 
stations in all sorts of places could be used with their 
proper weight. All the photographs could be measured 
by the same micrometer, whose errors of all sorts could 
be very carefully examined.' 

To this Dr. De la Rue replied as follows : — 
^ With respect to the localities to be selected, the 
employment of the photographic method of observing 
transits of Venus has, as I have already stated, the 
advantage of rendering us independent of conditions 
favourable or indeed essential for eye-observations ; 
for a few photographs obtained at each station would 
afford the means of ascertaining the path of the planet 
and its position at any given moment ; and hence the 
proposal to determine the position of the planet's centre 
in relation to the sun's centre really includes the 
particular case contemplated by Major Tennant in the 
foot-note appended to his paper ; but it is possible 
that the sun might be obscured at the critical time, at 
one of the two stations selected.' 

In December 1869 I read before the Astronomical 
Society a paper, from which the following passages 
are extracts : — 

the positions at these instants, and not the nearest approaches to the 
sun's centre, which should be compared.' 



206 TFcAySITS OF VI-XUS. 

^ It is impossible to read Dr. De la Rue's account 
of the results of careful measurement applied to pho- 
tographs of the solar eclipses in 1860 and 1868 with- 
out recognising that we have in photography^ as 
applied to the approaching transit of Venus, one of 
the most powerful available means of determining the 
sun's distance. AVithin the last few years, solar pho- 
tography has made a progress which is very promising 
in regard to the future achievements of the science 
as an aid to exact astronomy. So that doubtless, in 
1874, astronomers ^^ill apply photographic methods 
to the transits of that year with even greater success 
than we should now be prepared to anticipate. It has 
therefore seemed to me that the photographic obser- 
vation of the comino; transit merits at least as full a 
preliminary inquiry as either Halley's or Delisle's 
method of direct observation. 

^ The result of an inquiry directed to this end has 
led me to the conclusion that photographers of the 
approaching transit should adopt for their guidance 
considerations somewhat different from those which 
have hitherto been chiefly attended to. 

' It is undoubtedly true, as Dr. De la Eue has 
pointed out, that the photographer of the transit can 
readily take a large number of pictures, and by com- 
binino; these, can ascertain w^th OTeat accuracv the 
path of Venus across the solar disc. And by com- 
paring the paths thus deduced for different stations a 
satisfactory estimate can be formed of the solar parallax. 



THE COMING TRAJs'SITS. 20/ 

I do hot wish to suggest any departure from this course 
of procedure. 

^ On the other hand, it is undoubtedly true, as 
Major Tennant has remarked, that the greatest effect 
of parallax will be obtained, for any two stations, 
when both stations — the earth's centre and the centre 
of Venus — are in one and the same plane. So far as 
those two stations are concerned, his remark is just, 
that it is the position of Venus at the instant when the 
stations are so situated, and not the nearest approach 
of Venus to the sun's centre, which should be com- 
pared. And further. Dr. De la Rue's comment on 
this, to the effect that his method in reality includes 
Major Tennant's, is also correct. In fact, there can 
be no doubt that the position of Venus at the particular 
instant referred to by Major Tennant can be far more 
exactly ascertained by a reference to the complete 
path of Venus for each station than* from any attempt 
to secure nearly simultaneous photographic records at 
stations far removed from each other. 

' But it appears to me that the method I am about 
to suggest, according to which the whole question will 
be reduced to the determination of a parallactic dis- 
placement of Venus on a line through the centre of 
the suq's disc, is the one by which the fullest assist- 
ance will be obtained from photography; while a source 
of error, which has not hitherto been specially con- 
sidered, will be practically eliminated. 

^ It must be remembered that in the comparison of 



20S TR Ay SITS OF VEX US. 

photographic records^ whether for the determinatioil 
of the path of Venus across the sun's disc at a par- 
ticular station, or for the comparison either of Yenus's 
apparent position or of her path as seen from two 
different stations, the accuracy of the results will 
depend in part on the certainty with which two or 
more pictures may be brought into comparison by 
means of a fiducial line or set of lines. It seems 
certain that no method can be devised by which all 
chance of error from this source can be eliminated. 
The great point would, therefore^ seem to be to render 
its effect as small as possible. 

' Xow, let us consider for a moment Major Tennant's 
proposition, as giving a convenient illustration of the 




B 
Fig. 42. — Illustrating the photographic and direct methods. 

effects of any error either in the position of the fiducial 
lines, or in bringing those belonging to two pictures 
into exact correspondence. Let fig. 42 represent the 
result of a comparison between two photographs of the 
sun. A B and c D are fiducial cross-lines common to 
both pictures ; a is the centre of Yenus for one pic- 
ture, b is her centre for the other : and on the exact 



THE COMiyO TRAXSITS. 



209 



measurement of a b depends the determination of the 
sun's parallax^ so far at least as these two pictures 
are concerned. Xow it is very obvious that if the 
lines A B, c D, for one picture, have not been brought 
into perfect correspondence with those belonging to 
the other^ the distance a h will be correspondingly 
affected. In fact, it would appear that if the usual 
methods for making the correspondence as exact as 
possible are followed, almost as large an error would 
be introduced through this cause alone as by errors in 
the measurement of a b, since the two processes — the 
measurement of cf b and the adjustment of the sets of 
cross-lines — depend on the very same circumstance^ 
the nicety^ namely^ with which the eye and the judg- 




Fig. 43. — Illustrating the pliotograpliic and direct methods. 



ment can estimate minute quantities of about the same 
relative dimensions. 

' But now^ if a and b, in place of having the position 
shown in fig. 42^ were situated as in fig. 43^ it is clear 
that the distance a b will not be appreciably affected 
by any small error in the adjustment of the fiducial 
lines. 



210 TRANSITS OF VEXUS. 

^ The object^ therefore, which it seems most desi- 
rable to secure is that Venus, as seen from two dif- 
ferent stations at a particular instant, should have a 
relative parallactic displacement towards the sun's 
centre, or as nearly towards the sun's centre as possible. 
This amounts to adding to Major Tennant's conditions 
this further one, that the sun's centre should be in the 
same plane with the two stations — or rather to making 
this condition a substitute for that one which requires 
that the earth's centre should be in the same plane 
with the two stations. For, as a rule, we must not 
expect to be able so to arrange matters that two con- 
venient stations on the earth, as well as the centres 
of the earth, Venus, and the sun, should be in the 
same plane. 

^ Dr. De la Kue's remark, that by taking a series 
of pictures the position of Venus may be ascertained 
at any moment, is in reality quite as applicable to my 
suggestion as to Major Tennant's. In fact, were it 
not, we might despair of securing the desired object, 
since we have no reason for believing that astronomers 
are so certain as to the exact progress of the transit 
that the conditions could be secured by anticipatory 
instructions : whereas, by applying Dr. De la Rue's 
method, it will be possible, after the transit is past, to 
determine the position ofVenus at the proper instant 
Avith any desired degree of accuracy. And further, 
it is very obvious that no error in the placing of the 
fiducial lines for pictures taken at the same stations 
can much affect the accuracy of the result, since the 



THE COMING TRANSITS. 211 

comparison of successive pictures, taken at the same 
station, does not directly involve the element of the 
solar parallax, as when we have to compare two pic- 
tures or paths determined at different stations. 

^ The object which Plate XVI. was originally in- 
tended to subserve was to determine what stations 
are most suitable for applying photography to the 
transit of 1874, on the principles above enunciated ; 
though, as we have seen, the drawing presents also an 
instructive illustration of the whole character of the 
transit.' 

In Chapter IV., in pp. 148-152, I showed how all 
the chief elements of the transit could be deduced by 
considering the motion of Venus relatively to a pair 
of cones, each enveloping the sun and the earth, but 
one having its vertex outside the earth, the other 
having its vertex between the earth and the sun. In 
the paper from which I have been quoting, after ex- 
plaining the construction of Plate XVI., I proceeded 
as follows : — 

' We have only to invert fig. 35, and look at it 
from behind, to see what sort of path Venus would 
seem to traverse upon the sun's disc, either with 
reference to the earth's centre, or to any point of the 
earth's surface supposed to be properly depicted upon 
the small discs 1-15 in fig. 35. 

' It follows, therefore, that if we want to determine 
two stations at which at any instant Venus would 
appear to have a relative parallactic displacement 
towards the sun's centre, all that is required is that 

r2 



212 TRAXSITS OF VENUS. 

we select two stations which are on the same radial 
line from the common centre of the circular sections 
in fig. 36. 

' The positions of those radial lines which cross the 
earth's track c d are exhibited in Plate XVI. 

^Passing over pictures 1 and 2, we notice in pic- 
ture 3 that Kerguelen's Land and Crozet Island, 
lying nearly on a line with certain of the Aleutian 
Islands, suggest that pictures taken at the former 
stations at the bes^innino; of the transit could be ad- 
vantageously compared with pictures simultaneously, 
or almost simultaneously, taken at a station on one of 
the easternmost of the Aleutians. In like manner 
pictures taken near Enderby Land could be advan- 
tageously compared with pictures taken at Woahoo. 
Projection 4 does not differ much from the preceding, 
but the cross-lines have assumed a less inclined posi- 
tion, and Kerguelen's Land could, at the epoch be- 
longing to this picture, be better combined with a 
somewhat more westerly Aleutian island. Projection 5 
exhibits the advantage of a photographic station at or 
near Yokohama. Probably such a station, combined 
Avith one in Crozet Island or Kerguelen's Land, would 
give (by pictures taken near the hour belonging to 
Projection 5) absolutely the best results which photo- 
graphy can give. The remaining projections suggest 
the following combinations of photographic records : 
Projection 6. Yokohama and Heard Island, Kergue- 
len's Land and a station in Manchooria ; Crozet Island 
and Pekin ; Cape of Good Hope and Xertschinsk. 



THE COMIXG TF.AXSITS, 213 

Projection 7. Kergueleu's Land and Tsitsikar; Crozet 
Island and Xertschinsk ; Cape Town and a station 
west of Lake Baikal. Projection 8. Kerguelen's 
Land and Xertschinsk ; Cape Town and Pesbawur, 
or Eoorkee ; Eepulse Bay or neighbourhood and 
Yokohama; Perth (Australia) and Yokohama. Pro- 
jection 9. Yokohama and Perth; Enderby Land and 
X'ertschinsk ; Crozet Island and Calcutta: Cape Town 
and Bombay. Projection 10. Kerguelen's Land and 
Calcutta ; Crozet Ishmd and Pesbawur ; Cape Town 
and Teheran. Projection IE Kerguelen's Land and 
Madras; Crozet Inland and Pesbawur; Cape Town 
and Aden. Projection 12. Kerguelen's Land and 
Pesbawur: Crozet Island and Teheran. Projection 
13. A Xew Zealand station and Yokohama ; Hobart 
Town and a station near the mouth of the Amoor. 

' From this list we see that Kerguelen's Land and 
Crozet Island. Feshawur and other Indian stations. 
and stations in Siberia, are those wbicli give the most 
favourable opportunities for the application of the 
photooTaphic method.' 

The considerations described in the preceding pas- 
sage were those followed in the selection of stations. 

So far as preliminary inquiries are concerned, it 
remains only to be mentioned that most of the nations 
proposing to take part in the observations have made 
experiments on the phenomena of contact by means of 
an artificial transit. Although the results obtained at 
Greenwich are not altogether so satisfactory as they 
nno:ht be. owino- to the short distance from the ob- 



214 TRANSITS OF VEXUS. 

server at which the artificial discs have been placed, 
yet they only differ in degree, as presented in the 
folloAving passage, from the more marked peculiarities 
observed at Washington (where I studied the phe- 
nomena myself) : — 

1. It requires considerable experience for an ob- 
server to appreciate all the definite changes of appear- 
ance which occur. 

2. When two observers describe a particular phase 
which they see, and determine to observe this phase 
together, the times recorded by each are generally 
accordant within a fraction of a second. 

3. The successive phases of an ingress or egress 
appear to follow each other sometimes rapidly, at 
other times gradually; so that in some cases all the 
})henomena are observed within three seconds, on other 
occasions the same series of phases is completed in ten 
seconds. 

4. The time at which any particular phase is ob- 
served varies very slightly with the aperture of the 
telescope. When a telescope of good definition is 
employed, the time of any phase at ingress is earlier 
than with an instrument of less perfect definition. 

Observations such as these must necessarily serve 
to diminish the error of contact observations, especially 
as the observers will not only measure the distances 
between the cusps as contact proceeds, but will cause 
the phenomena of contact to be indicated photographi- 
cally by an ingenious arrangement contrived by Janssen. 
I think it not at all unlikely that the probable error of 



THE COMING TRANSITS. 21 5 

a contact may thus be made at least as small as the 
probable error of longitude determination. In this 
case the value of Halle j's method will be largely 
superior to that of Delisle. 

I turn next to the consideration of the plans of the 
various nations taking part in the observation of the 
transit of next December. Before reading what follows, 
the student will find it well to examine Plates VI. and 
VII. successively, after the manner indicated at p. 48, 
for the transit of 1761, and at p. 70 for that of 1769. 
Plates XIL, XIII., and XVI. should also be exa- 
mined. 

To America the pride of place must in fairness 
be conceded. She might reasonably have contented 
herself with but slight efforts on the occasion of this 
transit (because the transit of 1882 will fall pre- 
eminently to her share). But the i^merican Govern- 
ment has voted a sum (30,000/.) twice as great as that 
which has been granted by the British Government ^ 
for the purpose. Then, as I have already mentioned, 
America has undertaken the most difficult of all the 
tasks which the proper observation of the transit 
rendered necessary — I mean the occupation of the 
Crozets. Moreover, the preliminary investigation of 
the conditions of the transit by American astronomers 
is altoo^ether excellent. 



^ It must be noted, however, that our G-overnment unhesitatingly 
granted all that the Astronomer Eoyal asked, so that it \rould be alto- 
gether unfair to accuse the British Grovernment of stinginess in the 
matter. 



2l6 TJ^ Ay SITS OF VENUS, 

I have before me as I write the series of charts pub- 
lished by the American Commission appointed to inves- 
tigate the circumstances of the transit. These consist of 
four finely-executed stereographic charts showing that 
hemisphere (and a fringe beyond) on the earth which 
is turned sunwards at the time of (1) ingress exterior 
contact^ (2) ingress interior contact, (3) egress interior 
contact^ and (4) egress exterior contact. On these 
charts are marked two series of curves, one carried 
through points where the contact occurs at the same 
instant, and the other carried tli rough points where 
the contact occurs at the same part of the sun's limb. 
After a careful study of each chart (a study as careful 
as that which I gave to the Astronomer-Royal's charts 
in 1869), I am able to pronounce them singularly 
accurate for the degree of approximation which the 
authors claim. ^ 

The American astronomers are disposed to rely 
chiefly on the photographic method, applied at 
stations irhere the whole transit can he seen. The con- 
dition italicised is of some importance as indicating a 



^ There is a very elaborate investigation of the error actually arising 
from the use of circles for the time-curyes in the projection, to represent 
curves Avhich are not in reality circles of the terrestrial sphere. The 
maximum error is found not to be more than 12', which, says the author 
of the paper, • having regard to the scale on which the charts have been 
constructed, may be considered as within the unavoidable errors pro- 
duced by imperfection of drawing.' The maximum error is four times 
as great when the curvature of Yenns's shadow-cone is altogether neg- 
lected in the usual way, according to which the resulting time-error is 
always of one sign. In the American charts the error is so distributed 
as to be positive or negative according to circumstances. 



THE COMING TRANSITS. 21/ 

distinction between two possible photographic methods, 
one corresponding to Delisle's, the other to Halley's. 
The English arrangpments, for example, include the 
application of photography at the SandAvich Islands, 
where only the beginning of the transit can be seen, 
and at Alexandria, where only the end can be seen. 
Such photographs can, of course, only have value when 
the absolute time at which each is taken is accurately 
known. On the other hand, the American stations 
are so selected that photographs can be taken through- 
out the whole continuance of the transit, and these, 
by indicating the chords of transit, will have a value 
independent of the exact determination of absolute 
time; se that, in fact, the original error of the 
Astronomer Royal ^I mean the .particular error relating 
to Halley's method) would, if not corrected, have 
affected the application of the photographic as well as 
other methods. Fortunately, the American astro- 
nomers have not been misled by it,^ and at all the 
stations they propose to occupy, the whole transit will 
be visible, as will presently be more particularly noted. 
The plan they adopt for photographing the sun 
differs essentially from that which European astro- 
nomers propose to employ. ^ For the purpose of 

^ At the same time I must remark, tliat it seems to me altogether 
proper that the Delislean stations in question should be occupied by 
photographers. "What I have all along insisted upon has been, the 
necessity of employing every available method, and occupying every 
available station ; and it ^'ould have been a matter to be regretted, 
had any one of the regions originally suggested by Sir Gr. Airy been 
neglected. 



2l8 TRAXSITS OF VEXUS. 

obtaining an enlarged image on the photographic plate/ 
writes Professor Hilgard, of Washington, (describing 
the ordinary method). ^ the image of the sun. after 
being formed in the focus of the telescope, is enlarged 
by a lens or camera to the desired size, the photohelio- 
graphs, as they are called, being thus enlarged to a 
diameter of about four inches. This plan has been 
adopted for the photographic apparatus to be used by 
the British, German, and Russian parties commissioned 
to observe the transit of Venus. A diifiereut plan has, 
however, been adopted for the American parties, with 
the view of avoiding some difficulties to which the 
former method may be thought subject. These are 
conceived to reside in the fact that not only all imper- 
fections in the focal image are thus enlarged, but that 
the optical imperfections of the camera are superadded 
To avoid this objection it was deemed best to make 
the telescope so long that the image formed in its 
prhicipal focus would need no further enlargement. 
Here another difficulty presented itself. The telescope 
must be forty feet in length in order to give an image 
four inches in diameter. Such a telescope, pointed at 
the sun, would scarcely be manageable. Hence the 
plan was devised, which Professor TTinlock was the 
first to put into practical operation. It consists in 
fixing the long telescope in a horizontal position, and 
reflecting the sun's rays into the object-glass by means 
of a plane glass mirror, moved by clockwork, so as to 
throw the image of the sun continually into the tele- 
scope. This need nor be done with great precision. 



THE COMING TRANSITS. 2ig 

since^ as has already been said, the time of exposure is 
exceedingly small, and the mirror can at any time be 
adjusted. It is obvious that, in this arrangement, as 
much depends upon the perfect figure of the mirror, 
as in the other upon that of the enlarging lens ; but 
it is, doubtless, an advantage that different methods 
should be employed, so long as a sufficient number of 
stations are occupied to give an independent result for 
the sun's distance from observations by each method 
alone, since such only can be considered as strictly 
comparable. This condition is amply fulfilled by the 
abundant provision made by the American Govern- 
ment for the observation of the important event in 
prospect.' 

I may remark, however, that Professor Newcomb, 
with whom I had the pleasure of a conversation rela- 
tive to the subject, attaches very great importance to 
the advantao-es of the American method. He remarked 
that by employing this method the astronomer is 
enabled to measure the distance of Venus from the 
sun's centre with an exact knowledge of the value of 
the deduced distance, because, the focal length of the 
telescope being known, the value of any distance indi- 
cated in the focal image is at once determined. All 
that is necessary, then, is to determine the centre of 
the solar image, which can be safely done by measure- 
ments made from the limb. Manifestly no photographic 
effects affecting the position of the limb in the photo- 
graph could appreciably affect the determination of the 
centre even though such effects were not absolutely 



220 TRANSITS OF VENUS. 

uniform all round. But In the ordinary method of 
photographing the determination of the arc-distance of 
Venus from the centre is not reliable (in a problem of 
such extreme delicacy), because the estimated dimen- 
sions of the solar image could not be accuratehj 
determined, while the observed dimensions, being 
determined from the photographic limb of the sun, 
would be affected more or less by photographic irradi- 
ation. No apparent sharpness of the limb can render 
certain the fact that the limb in the photographic 
image corresponds to the true solar limb. I must 
confess that Professor Newcomb's reasoning seems 
to me irresistible. It will be observed that it does 
not depend on practical or technical knowledge of 
photography, since the photographic irradiation demon- 
strably exists, and is demonstrably variable in amount. 
In a conversation with Dr. H. Draper, of New York, 
whose experience in those matters is well known to be 
unsurpassed, I found Professor Xewcomb's doubts 
fully confirmed. It is true that Dr. Rutherfurd, 
whose great practical experience in solar photography 
is unquestioned, agrees with his eminent British rival 
in such work, Dr. De la Rue. But then it is to be 
remembered that both Rutherfurd and De la Rue view 
the matter as photographers, while Newcomb and 
Draper view it chiefly from an astronomical standpoint, 
and in this case the astronomical, not the photographic 
relations, are chiefly in question. We dp not want 
handsome solar pictures, but pictures which can be con- 
fidently measured ; and certainly the plan adopted by 



THE COMING TRANSITS. 221 

American astronomers is that which best meets this re- 
quirement. I may add that a very eminent American 
astronomer, speaking to me on this subject, made 
this strong remark, ^I regard the photographic method 
adopted by the British astronomers as involving a mis- 
take as fatal as Airy's original mistake would have 
been if uncorrected.' ^ 

The programme of the American expeditions is as 
follows : — 

Eight parties take the field, three in the northern 
hemisphere, ' where the meteorological conditions are 
supposed to be somewhat more favourable than at 
corresponding stations in the southern hemisphere,' 
where there will be five. The three northern stations 
will be (1) at Vladivostok, in Siberia; (2) at Tien- 
tsin, in China; and (3) at some as yet undetermined 
place in Japan. Originally, in response to the strongly 
expressed wish of the Astronomer Royal that two 
Delislean stations should be occupied, one on the 
Sandwich Islands group, and another at Tahiti, the 
Americans thought of occupying Owhyhee, rejecting 
as disadvantageous the suo-o-ested Tahitian station. But 
since then the idea of having any Delislean stations 
has been abandoned, and, as just mentioned, the five 
remaining stations are all to be in the southern 
Halleyan region. ' The " Swatara,-' ' says an American 
paper, ' the vessel which is to convey the various 

^ Lord Lindsay, it is to be noted, will employ the same method as 
the American astronomers, after carefully testing with Mr. Ranyard, in 
a series of photographic experiments, the reliability of the two methods. 



222 TEAXSITS OF VENUS. 

southern observing parties to their stations/ sailed from 
^ew York during the first week of June, and is ' to 
lay in provisions at Cape Town, as well as a supply of 
hens for the sake of their eggs, wherewith to albumenise 
the photograph plates. Then a party will, weather 
permitting, be left at the Crozet and Kerguelen Islands. 
As in frequent conditions of the wind access to the 
Crozet Islands is impossible, enough provisions will be 
left with the observers, and possible prisoners, to last 
them a whole year. From Kerguelen the vessel will 
sail to Hobart Town, thence to Bluff Harbour, in Xew 
Zealand, and thence to Chatham Island, the last 
southern point of observation, which is either unin- 
habited or else inhabited by cannibals. Here the 
^ Swatara ' will remain till the transit is over, and will 
then, the possible cannibals allowing, re\dsitthe various 
stations to take up the different parties, supposing 
them to be found.' ' Each station will be provided 
Avith four principal instruments : The photographic 
telescope just described, with a 5-inch object-glass 
corrected for the actinic rays, and forty feet local 
length : a telescope of five inches' aperture and eight 
feet local length, equatorially mounted for the ob- 
servation of contacts ; a transit instrument for the 
determination of time and geographical position ; and 
an astronomical clock. The telescopes, both visual 
and photographic, have been ordered from the well- 
known firm of Alvan, Clark, and Sons, who have just 
completed and mounted at Washington the greatest 
refractinjo; telescope in the world. Although the 



THE COMIXG TRANSITS. 22$ 

photographic method is mainly relied on, the eye- 
observations of ingress and egress are not to be 
neglected, and it is proposed to supplement them by 
measuring the distances of the cusps ^vhile the planet 
is enterino; the sun's disc and leavino; it/ This last 
point I regard as one of extreme importance, as will 
be gathered from my remarks on the subject in ' The 
Sun,' and in the Monthly Notices of the Astronomical 
Society, yoh xxx. p. 46 et seq. 

While all the American stations^ as well northern 
as southern^ are Halleyan, the English stations 
originally selected, were all intended to be used solely 
as Delislean stations. In fact, as already seen, in 
dealing mth those among them which really are 
Halleyan as well as Delislean, Airy failed to notice 
that both ino;ress and egjress can be observed. 

Nine stations have been provided for, eight by the 
Home Government, and one by the Indian Govern- 
ment. Originally five stations were to have been 
occupied. 

It is well to note, first, that ample provision has 
been made for the application of Delisle's method. 
No less than three stations ^411 be occupied in the 
group of the Sandwich Islands, where Captain 
Tupman (the head of the entire enterprise) will be 
stationed.^ Here photography wiU be applied specially 

* In an excellent article (though not quite free from mistakes) in tlie 
'London Quarterly Ee\dew,' the writer justly speaks of Captain Tupman 
as the ' moving spirit and master of the whole enterprise.' The success 
of the English expeditions ^ill be chiefly due to the zeal and energy of 
Captain Tupman. 



224 TRANSITS OF VEXVS. 

to the determination of the moment of inofress, bv a 
contrivance of Janssen's (improved by De la Rue) 
enabling the photographer to take sixty successive 
pictures of the ingress, at the rate of one per second. 
Under Captain Tupman's command will be Lieutenants 
Ramsden and Noble, and Messrs. Johnson, Forbes, 
and Barnacle. The observation of accelerated ingress 
has been well provided for, especially as some of the 
H alley an stations in Japan and the north-east of Asia 
are excellent for this phase also. 

Retarded inoTess will be observed at Kerg-uelen's 
Land and Rodriguez. According to the published 
statements there will be two stations on Kerguelen's 
Land, but Fr. Perry, who is chief in this region, has 
power to assign one party to Heard Island if a landing 
shall be found to be practicable. The three stations 
here are all Halleyan as well as Delislean, the whole 
transit being most favourably visible. It is well, 
therefore, to note that ample provision has been made 
for applying Halley's method, as well as for photo- 
graphing the whole progress of the transit. The ob- 
servers under Fr. Perry Avill be Fr. Sidgreaves, 
Lieutenants Corbet, Goodridge, and Coke, and Mr. 
J. B. Smith. At Rodriguez, Lieutenants Neate and 
Hoggan, and Mr. C. E. Burton, will be the ob.«ervers. 

Accelerated egress will be observed at Christ- 
church, New Zealand, by Major Palmer and Lieu- 
tenants Darwin and Crawford. This station, like 
the stations for observing retarded ingress, is Halleyan 
also, and is now well provided for as a station for 
observino; the whole transit. 



THE COMING TRANSITS, 225 

Retarded egress will be observed at Alexandria 
by Captains Browne and Abney, and Mr. S. Hunter. 

The transit will be observed at Roorkee^ in North 
India by Colonel Tennant. The whole transit will be 
observed at that station^ and photoi>;raphy employed. 
Mr. Pogson will observe the transit at Madras. At 
Colaba, Mr. Chambers will observe the transit Avith 
such instruments as were left there by the observers 
of the late Indian eclipse. 

The total cost of the British expeditions, exclusive 
of the Indian station, will be about 15,000/. 

Lord Lindsay's station at Mauritius must be 
mentioned in this connection. The work done there 
will probably be quite as reliable as that done at 
any other station, and the photographic preparations 
are, on the whole, more complete than those adopted 
anywhere else. 

It may be mentioned, also, that Colonel Campbell 
will proceed to Thebes on a private expedition, work- 
ing Avith the Egyptian party as a volunteer. 

German astronomers occupy five southern Halleyan 
stations, one of these being either the desolate Heard 
Island, or Kerguelen Land (if, as is feared. Heard 
Island cannot be occupied). Their original purpose 
was to occupy one station in the north, viz. at Chefoo, 
in China, one in the Auckland Tslands, and Macdonald 
Island, besides a photographic station in Persia. They 
will rely considerably on the ' direct method ' of obser- 
vation. 

The following account of the plans of Russia, 
Q 



226 TRANSITS OF VEXUS, 

France, and Holland is taken from the excellent 
article in the ' London Quarterly Review/ referred to 
in the note at p. 193 : — 

* The Russians naturally occupy their own Siberian 
stations. It is possible that some little service may 
be rendered at Kazan, Xicolaief, Charkof, Odessa, and 
even Moscow. But apart from these there are to be 
twenty-six stations ; but of these only the following 
will be supplied with a complete equipment of ob- 
servers and instruments, viz. Wladivostock, Port 
Possiet, Lake Hanka, Xertschinsk, Xhita, Kiachta, 
Tachkent, Port Peroffski, Fort Uralsk, Aschura-deh, 
and Erivan. These stations will be furnished with 
astronomers, who are prepared by work with the 
artificial transit, and who are furnished with excellent 
equatorials with clockwork motion, a heliometer, or a 
photographic apparatus. The other stations are to be 
provided with good observing telescopes, and the re- 
mainder merely with small instruments. At eleven of 
the stations both inm'ess and eo:ress will be seen, so 
that the Halleyan method may be employed ; and at 
the remainder of the stations they will be chiefly 
concerned with retarded egress. M. Struve also has 
visited this country, as well as others, that compari- 
sons might be made and greater accuracy secured. 

' The stations chosen by the French are Campbell 
and St. Paul's Islands, Houmea, Pekin, Yokohama, 
and Saigon. M, Janssen goes to the Yokohama 
station, and this station in connection with St. Paul's 
will be almost perfect for the Halleyan method. But 



THE COMIXG TRANSITS. 22 J 

o;reat care is to be taken in the findlno- of lono-itudes ; 
SO that if only ino-ress or eo-ress can be observed, the 
Delislean method may be employed. It is also an 
important matter that the French photographs Avill be 
taken by the Daguerreotype process^ ensuring delicacy 
and avoiding the difficulties possible to the shrinkage 
of the film employed in other methods. The parties 
at St. Paul's and Campbell Islands — placed as they 
will be on islands of desolation — are furnished with 
fuel and provisions for six months. Originally the 
sum granted was 300,000 francs ; but this is to be 
considerably augmented, and there may certainly 
be excellent results anticipated from this national 
effort. 

' Finally, the Dutch are sending out an admirably 
equipped expedition to the island of Reunion. It is 
to be provided with a very fine heliometer and a 
photo-heliograph by Dallmeyer, like those used by 
Enofland ; and two excellent refractors for observation. 
They will also be furnished with meteorological instru- 
ments and all apparatus necessary for finding longi- 
tude and time.' 

So much for the preparations on foot for the transit 
now near at hand. As regards the transit of 1882, 
it would be premature to speak. It is to be hoped 
that what has happened in the case of the transit of 
the present year will serve in some sense as a warning 
to astronomers not to place implicit reliance on the 
opinions of any astronomer, however deservedly emi- 
nent, and also to prevent any unduly hasty expression 

Q 2 



228 TI^AXSITS OF VEXUS. 

of opinion by persons whose official position would cause 
the admission of error to be unpleasant. Adding to this 
consideration the fact that a large amount of practical 
experience in the value of the various methods of 
observation will probably be acquired during the ap- 
proaching transit^ we may well hope that in 1882 even 
more valuable observations will be made. It needs but 
a short study of the sun- views forming Plates XIV. 
and XV, (or, preferably in some respects, figs. 37 
and 38), and of the stereographic projection Plate VII., 
to see that American astronomers will have to take by 
far the most important share in the work of observation 
in tlie northern hemisphere. May it be permitted to 
me, however, to hope that England, by well-considered 
expeditions to southern stations, will remove any 
doubts that other nations may have entertained as to 
her zeal for science ? 

I may note here that while Halley's method fails 
totally for the transit of 1882, a method which, in 
some degree, would take its place may be applied 
with considerable advantage if stations in Patagonia, 
Tierra del Fuego, the Falkland Isles, or, better still, 
the sub-Antarctic islands directly south of Cape Horn, 
could be reached. I refer to a method which may be 
called the mid-transit method, and which consists in 
the determination (preferably by photography) of the 
distance of Venus from the sun, near the middle of 
the transit, at two stations where the difference of her 
distaiice from the sun's centre will be the greet test 
possible. It will be manifest to the student, if he 



THE COMING TRANSITS. 22Cj 

considers what I have said in pp. 209^ 210^ that 
the advantages claimed for stations on a radial line 
through the centre of Venus's shadoAv-cone (o in fig, 36) 
culminate when the earth is near the centre of her 
chord of passage through the shadow-section v v^ 
Wherever convenient stations exist for advantageously- 
photographing the whole chord of transit, it would of 
course be absurd to select a station only advantageous 
for the middle of the chord ; but in the transit of 1882 
the whole chord cannot be very advantageously photo- 
graphed at southern stations ; and there will be a 
decided advantage in securing mid-transit photographs 
(as well, of course, as photographs of the beginning 
and end, and series of photographs for the whole transit 
w^here practicable). 

However, for the present we need not inquire 
very closely into the conditions of the transit of 1882. 
Probably, long before that transit, the observations of 
the remarkable opposition of Mars in 1877, referred 
to in my ^ Sun 'at p. 25, will have given results 
scarcely less trustworthy than those obtained during 
the approaching transit. 

It is not probable, judging from what Sir G. C. 
Lewis has shown respecting centenarians, that any of 
my readers will witness the transits of 2004 or 2012. 
Nevertheless, it may be interesting to know the cir- 
cumstances of those transits and the regions of the 
earth where they will be wholly or partially visible. 
Mr. Hind, Superintendent of the Nautical Almanac, 
has calculated the elements of the two transits of the 



230 TRANSITS OF VENUS. 

beginning of the twenty-first century. His results 
are thus presented in the Notices of the Astronomical 
Society for February 1872, p. 184 : — ^ 

Transit of 2Q0^. 

Greenwich Mean Time of Conjunction in Right 
Ascension = June 7^ 20^ 5 1"' 28*-8. 

For the centre of the Eirth. 

d h m s ° 

First external contact Jnne 7 17 3 43 at 115*0 

First internal contact „ 17 22 35 „ 118 

Second internal contact „ 23 5 40 ,, 214-6 

Second external contact „ 23 24 32 „ 218-5 

The ano-les are reckoned from X. towards E. for 

CI 

the direct image. 

At Greenwdch the entire transit will be visible. 

Transit of 2012, 

Greenwich Mean Time of Conjunction in Right 
Ascension = June 5^ 13^ 4^ 44^-3. 

For the centre of the Earth. 

d h m 5 ° 

First external contact June 5 10 22 11 at 40*3 

First internal contact „ 10 39 56 „ 37*8 

Second internal contact „ 16 42 6 „ 293-1 

Second external contact ,, 17 0,, 290*5 

At Greenwich the egress only will be visible^ the 
sun rising at 15^ 46"^. 

' M. Le Terrier's TalDles of the sun and Venus represent so closely ' 
tlie motions of the earth and Venus in their orbits, that there can he 
little reason to doubt that the Tables will be as sensibly perfect, in 2J04 
as tlip'v are at the present time. 



THE COMIXG TjR^^XSITS. 23 1 

These results are illustrated by the projections 
forming Plates YIII. and IX. ^ and bj the transit 
chords shown in Plate I. (the Frontispiece). The 
reader who has followed the explanations of Plates 

IV. and V. will have no difficultv in understand- 

t/ 

ing the plates illustrating the transits of 2004 and 
2012. 

VTe cannot doubt that when the transits of 2004 
and 2012 are approaching^ astronomers will look back 
with interest on the operations conducted during the 
present ^ transit-season ; ' and although in those times 
in all probability the determination of the sun's dis- 
tance by other methods — by studying the moon's 
motions^ by measuring the flight of lights by estimating 
the planets' weight from their mutual perturbations, 
and so on, will far surpass in accuracy those now 
obtained by such methods, yet we may reasonably 
believe that great Aveight will even then be attached 
to the determinations obtained during the approaching 
transits. I think the astronomers of the first years of 
the twenty-first century, looking back over the long 
transitless period which aWU then have passed, will 
understand the anxiety of astronomers in our own 
time to utilise to the full whatever opportunities the 
coming transits may afford ; and I venture to hope 
that should there then be found, among old volumes 
on their book-stalls, the essays and charts by which I 
have endeavoured to aid in securing that end (perhaps 
even this little book in which I record the history of 
the matter), they will not be disposed to judge over- 



232 TJRANSITS OF VHNUS. 

harshly what some in our own day may have regarded 
as an excess of zeal. 

Let it be hoped that the success of operations 
conducted by the various scientific nations in 1874 
and 1882 may be such, that preliminary difficulties 
will hereafter be remembered only as obstacles suc- 
cessfully removed and in good time. 



233 



TEANSIT OF 1874. 



Taule I. — Places where Ingress 
is accelerated. 



Table II. — Places where Ingress 
is reiardicL 



! 

station 


.3 

in o 


a'" J 

m 


Station 


.2 

02 % 




r 

Woahoo 


19-8 


m. 
11-2 


Crozet Island 


deg. 
15-0 


n 
12 


1. 
6 


Hawaii . 


19-7 


11-1 


Enderby Land 


20-0 


11 


•8 


\ Aitou Id., Aleutian 


10-8 


10-3 


Kerguelen Land . 


27-5 


11 


•6 


Marquesas Island . 


17-7 


7-9 


Macdonald Island . 


31-0 


11 


2 


Mouth of Amoor K. 


U-0 


7-6 


Kemp Island 


30-0 


11 


1 


Jeddo . 


32-1 


6-8 


Bourbon Island . 


12-4 


11 


•1 


Otaheite 


29-7 


6-4 


Mauritius 


U-1 


10 


*7 


Nertchinsk • 


10-1 


5-8 


Amsterdam Island 


34-1 


10 


3 


Tsitsikar 


17-0 


5-8 


Rodriguez 


19-0 


9 


9 


1 Kirin-Oida . 


19-5 


0-7 


Sabrina Land 


45-0 


8 


2 


Nagasaki 


32-7 


5-3 


Adelie Land . 


450 


6 


8 


Tientsin 


22-2 


5-0 


South Victoria Ld. 


38-5 


6 





Pekin . 


20-8 


4-3 


Perth (Australia) . 


65-0 


5 


3 


j Shanghai 


28-5 


3-9 


Eoyal Co. Island . 


62-0 


4 


5 


' Nankin. 


27-1 


3-6 


Madras 


21-0 


4 





Canton . 


35-0 


1-6 


Bombay 


12-0 


3 


8 


Hongkong . 


36-2 


1-6 


Macquarie Land . 


520 


3 


5 








Hobart Town 


670 


2 


8 








Adelaide 


75-0 


2- 


5 








Melbourne 


750 


2-2 



^34 



mAXSITS OF VFXUS. 



TRANSIT OF 1874. 



Table III. — Places irhere Egress 
is accelerated. 



Table IV. — Places wliere Egress 
is retarded. 



Station 


51 1 


ill 


Station 


■s. *^ 

'- > 

1 


ill 


St)urh Vietori;! Ld. 


1 
deg. i 


m. 




deg. 


m. 


i (Possession Ilud.) 


2.50 i 


1P4 


Oi*sk . 


12-0 


11 


8 


1 Adelie Land . 


34-0 


10-6 


Omsk 


IPo 


11 


/ 


Campbell Island . 


260 


10-3 


Astracau . 


120 


11 


6 


Emerald 


30-0 


10-3 


Aleppo 


' 14-6 


10 


5 


'. Macquarie Island . 


320 


98 


Pesha^mr . 


31-0 


10 


3 


; Chatham Island . 


16-0 


9-8 


Alexandria 


14-0 


10 





1 Canterbury (X.Z.) 


22-5 


9-3 


Suez . 


16T 


9 


8 


i Wellington . 


200 


9-2 


■ Xertchinsk 


lOT 


9 


8 


1 Sabrina Land 

j 


■430 


9 2 


Delhi 


38-0 


9 


4 


■ Enderby Land 


39-0 


8-0 


Tsitsikar . 


120 


8 


/ 


Eoyal Co. Island . 


420 


8-5 


Bombay . 


4o-0 


8 


5 


Auckland 


19-2 


8-0 


Pekhi 


21-0 


8 


6 


Kemp Island 


oPO 


7 6 


Kirin-Oula 


14-0 


8 


4 


Hob art To^vn 


40-0 


7-6 


Tientsin . 


i 17T 


S 


4 


\ Melbourne . 


43-0 


6-6 


Calcutta . 


45-3 


8 


2 


1 Sydney. 


37-2 


6-6 


. Aden 


; 30-0 


'' 


8 


1 Adelaide 


47-8 


0-8 


Xankin 


27-0 




6 


i Iverguelen Land . 


57-1 


o-O 


: Madras . 


o2-0 


7 


4 


: Crozet Island 


47-0 


4-2 


Shanghai . 


26-0 


7 





j Perth (Australia) . 


66-2 


3-6 


Canton 


' 37-0 


6 


6 


i 






Hongkong . 


37-0 


6 


5 



THE COMING TRANSITS. 



235 



^ 



S 



§ 



.2 
J 

1 
1 

1 

i 

! 

i 


zanS 
-Lipoa puB 
* epiBiapY 


Ci -H >p c'^ Cv) t^ C<J 1^- lO >^ -^ CO -M i 

2coc<ic<i^rUpl4bbciCicb<bcb»b ! 


siit:j. 

-UlTBJ^ PUU 

eiLinoqiai^ 




puBisi 

iioqjnog; 

piTU ('Z'K) 

Xinqja^u-BO 


r^ ^^ '^^ cc >_^ >p CO cc -M .-^ 1 

3''^'^-t^cococ^rc<1'^J4-l^^c^o6o^c^>. 


u.\iox 
i^reqoH 


t^ ^p oc <r) CO oc CO oc :p ?p >c -^^ CO 
gb^H'Vtcocococcj'f.irli^dooooci^ 


pm^isi 
puBi>[onY 


Ot^-'^GOOcOOOCOCO^^O'^-rH^ 

g do CO b »b »b lb -^^ -^ CO CO b b b Oi 


pn^isi 

•00 i-BAoa: 


OCO^-HOJCi-HCi-HC<l'M.-HOC5 j 

£ooi^i^bbib>b^-^^^rlH,lH,l^b i 


PUBISI 

Uaqdm'BO 


r^ -H '?<i ''^ CO ';t: >c CO CO 'N ^ 
goor-J^bbb'b'b-^'-^-rlHrl^rl^b j 


pui?T: 
au'Bnboi?]^^ 


£b^'^-bbb>b«b4^'^rll'^^l^b ' 

C<J'M'M0qc<JC<IC<10C|(M!M(M(MCqc<l 1 


PUT?ISI 

piBjarag- 


COOQOr^CiOr-I^Dr-lCiC^OOi^-Cp 

Sbooir-ir^bbb'b'b'^.— i-^-^b 


pu^T: 
U9pn°ja}j 


Oq Oi t^ 00 ^p i_0 00 00 1;^ >p 

S'f'iobbc7ibbocoor~--+'-+4ticb 

"•cOCOCOCOtM^MC^ICNC^lCMCNOqC^JC^J 


pui^isi 

PITJlIOpOB]^ 


COOOO-T-OCOr^Or-iCiCiOOt^cp j 

Sc<ir^bbbbboodcb-'^-^'i^^ 1 

'^COCOCOCO<MCqC<l<MCM(MC<IC^10qS^ j 


pii^isi 


-t^'-•Ci'^^Ol^-'^^^-c^ooc^oc^^ 

Scqrl^bbbbciooocoo>b-t"'*co | 

"^COCOCOCOCOC<JC<lC<l(NC<IC<JCv|C<IC<l ! 


pii^isi 


(M Ci J^ 00 vf:> ic^ 00 00 r- tp 
i ..'^cqc^io^rl-STlHr^bbbbbbo 

1 ScOCOCOCOCOCOCOCOCO'MC<J<MO<IC<I 









Novthorii 
Stations 




Nertcliinsk 
Tsitsikar . 
Kirin-Onla 
Tientsin 

Pekin 

Tchofoo 

Nagasaki 

Bonin Is. 

Nankin 

Canton 

Hongkong 

PcshaAvur 

Delhi 



236 



TFcAXSITS OF VFXUS. 



Table VI. 



For determining the effect of changes in the value of the Sun's equatorial 
horizontal jjarallax {at his mean distance) on the estirucited mean 
distance. 



\ Parallax ! 


Mean Distance 
(in miles) 


Difference for 0"-01 
(in mile?) 


; 8-0' i 


102.173,020 


126.142 


: 8-1 1 


100,911.600 


123.061 


8-2 


99.680.990 


120.097 


; 8-3 


98,480,020 


117.240 


8-4 1 


97.307;620 


114.478 


1 


96.162,840 


111.820 


: 8-6 


95,044.640 


109,244 


: S7 


93.952,200 


106,766 


; 8-8 


. 92,884,540 


104,362 


i 8-9 


91.840.920 


102 045 ^ 


9-0 


90.820.470 


99,805 


9-1 


89.822,420 


97.632 


9-2 


88,846.100 


95.532 


9-3 


87,890.780 


93.504 


9-4 


86.955.740 


91.530 


9-5 


86.040.440 


1 89.624 


9-6 


85,144.200 


; 87.780 


97 


84,266.400 


' 85.986 


" 9-8 


83.406.540 


84.248 


9-9 


82,564.060 


82.564 


100 


81.738.420 


' 



POPULAE SCIENTIFIC WOEKS 

By EICHAKD ANTHONY PROCTOK, B.A. Cantab. 

Honorary Fellow of King's College, London ; 

Honorary Secretary of the Boyal Astronomical Society, 



The UNIVEESE and the COMING TEANSITS : Pre- 

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' We heartily commend this book to the 
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The SUN; RULER, LIGHT, FIRE, and LIFE of the 

PLANETARY SYSTEM. Second Edition, revised; with 10 Plates 
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'This volume is a model of a popular 
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not only one of the clearest waiters who 
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science to the unscientific world, but is 
himself an original and laborious inves- 
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the discoveries about the centre of our 
system which the past few j'ears have 
produced. It is especially full on the dis- 
coveries as to the physical condition of 
the Sun which have been made by the 
observation of its total eclipse. The 
illustrations of the red prominences which 
stand out beyond the black shadow during 
the moment of total eclipse are exceedingly 
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conception of them than is to be gained 
by any other process, except that of 
actually seeing them through a powerful 
astronomical telescope. Mr. Proctor has, 
in fact, embodied and illustrated all that 
is known about the Sun ; and at the same 
time has given a pleasant hist ry of all 
the steps towards these discoveries, and a 
clear indication of the direction in which 



he thinks further discoveries will be 
made. Mr. Proctor tells us what i- 
known and what is only guessed, and 
enables us pretty fairly to appreciate the 
real value of the guesses. The Author's 
power of giving a clear statement of a 
very complicated problem is perhaps best 
ilhistrated in the section devoted to the 
question of the Sun's distance. It is not 
only the fullest but the clearest popular 
account of the methods and the result of 
his investigation which has ever been pub- 
lished. The object of the volume is to 
fu^-nish a full account of the remarkable 
discoveries which have been effected by 
observers of the Sun, whether bj means 
of the telescop?, the spectroscope, polari- 
scopic analysis, or photograuhy. This is 
accomplished not merely by Mr. Proctor's 
letterpress, bat by ten lithographic plates, 
of which seven are worked in colours, and 
one hundred and seven drawings on wood. 
This profusion of pictorial illustration 
makes the book very valuable." 

Daily News. 



London, LONGMANS & CO. 



Worl's bij R. A. Proctor, B.A. 



The SUN ; an Account of the Principal Modern Dis- 
coveries respecting the structure of the Sun of our System, its 
Influence in the Universe, and its relations with respect to the other 
Celestial Bodies. By F. Secchi, S.J. Director of the Observatory of 
the Roman College. (Translated and edited by ]VIr. Peoctor.) 
1 vol. 8vo. \^In the lyess. 

The MOOX ; Her Motions, Aspect, Scenery, and Physical 

Condition. With 22 Lithographic Plates, Charts, and Diagrams, 
1 \Yood Engraving, and 3 Lunar Photographs by Rutherfurd of New 
York. Crown 8vo. price 1 os. 

The STAE DEPTHS, or OTHER SUNS THAX OURS ; 

a Treatise on Stars, Star Systems, and Star Cloudlets. Crown 8vo. 
with numerous Illustrations. \_In the press. 

LIGHT SCIENCE for LEISUEE HOURS, Second 

Series ; Familiar Essays on Scientific Subjects, Natural Phenomena, 
&c. including a Sketch of the Life of Mary Somerrille : with 7 
Charts and Diagrams. Crown 8vo. price 7^. 6d. 

LIGHT SCIENCE for LEISUEE HOUES; Familiar 

Essays on Scientific Subjects, Natural Phenomena, &c. Second 
Edition thoroughly revised of the Pibst Series. Crown 8vo. 7s. 6d. 

*DiTested of both technicality and ex- i to sift those questions that others have not 

cessive simplicitT, there is conveyed to the i the opportunity of even nieetino: with — a 
reader of this coliection of Essays an im- true interpreter, who learns nature's lan- 
mense amount of information. .. .It is such guage not for himself alone. Mo>-t of 
works as these from the pen of Mr. Proc- these essays have been before the public in 
TOR that silence the cry of cni bono un- another form, but there is not one that 
happily prevalent. We cannot all be would pall upon a second perusal ; while 

scholars in the limited meaning of the ] some, published in a college magazine, are 
word, but we may all be scholars in the new to the gene] al reader. The subjects. 
s;hool of Xatuue, learning to read what are so various that he must be hard to 
is present to all our senses. It is this that please who does not find sufficient to in- 

Mr. Proctor does — brings a cultured brain , terest him in the volume.' 

JouiiXAL of Science. 



London, LONGMANS & CO. 



Works bi/ R. A. Proctor, B.A. 



OTHER WORLDS THAN OURS; the Plurality of 

AYorlds studied under the Light of Recent Scientific Eesearches. 
Third Edition, revised and enlarged; with 14 Illustrations. Crown 
8yo. price lOs. 6cL 

'Probably no science diu-ing the last 
few years has made such rapid strides as 
astronomy. This advance is mainly owing 
tD the discovery of the spectroscope, and 
its application to astronomical purposes. 
That wonderful instrument, more wonder- 
ful, perhaps, than the telescope, may be 
properly termed a liglit'Sifter, and is used 
to analyse the light which comes to us 
from other orbs across the ocean of space, 
so as to set before us their general cha- 
racter and structure. The Author of the 
present work attempts to make use of the 
startling disco reries effected by the aid of 
the spectroscope, in order to form juster 
views of the structm'e and relations of 
the planetary and stellar systems. H? 
again raises the question of the plurality 
of worlds, which a few years ago employed 
the scientific and dialectic skill of such 
men as Dr. Whewell and Sir David 
Brewster, and ages before fascinated the 
early philosophers of ancient Greece. Mr. 
Proctor considers that science has pro- 
gressed so rapidly of late that the subject 

The ORBS AROUND US ; a Series of Familiar Essays 

on the Moon and Planets, Meteors and Comets, the Sun, and Coloured 
Pairs of Stars. Second Edition, with Chart and Diagrams. Crown 
8vo. price 7^. Qd, 

essays on ASTRONOMY: a Series of Papers on 

Planets and Meteors, the Sun and Sun-surroanding space, Stars and 
Star Cloudlets ; and a Dissertation on the approaching Transit of 
Venus ; preceded by a Sketch of the Life and AVork of Sir John 
Herschel. With 10 Plates and 24: Engravings on Wood. 8vo. 
price 125. 

' To those who wish to learn some of 
the great results ^-hich have been recently 
achieved in astronomical science we 
heartily recommend the volume. Although 
Mr. Proctor writes in a popular manner, 
his sketches are evidently based on a care- 
ful investigation of the subjects in their 
scientific aspect, and are not mere turgid 
addresses on the silent stars and the glori- 
ous orbs of heaven. He is an astronomer 



of life in other worlds has assumed a new 
aspect since AVhewell"s Pluraliti/ of 
Worlds and Brewster's Jfore Worlds 
than 0«e were written. Arguments which 
were hypothetical thirty years ago have 
either become certainties or been dis- 
proved. Doubtful points have been cleared 
up ; a new meaning has been found even 
in those facts which were well known to 
both the disputants ; and, lastly, a new 
mode of research has been devised, which 
has not only revealed a number of sur- 
prising facts, but promises to work yet 
greater marvels in the years which are to 
come. Certainly Mr. Proctor has taken 
some pains and trouble to expound and 
illustrate his arguments and theories ; and 
his work shows, moreover, much patient 
research and wide scientific reading. If 
we are occasionally compelled to differ 
from some of his conclusions, we cannot 
deny the fact that he has produced a most 
interesting work on a very fascinating sub- 
ject.' EXA31IXER. 



himself, one of those laborious observers fol- 
lowing in the footsteps of the Herschels, 
and not a mere theorist and poetical 

populariser The papers on the 

Planets, Meteors, and Shooting Stars, the 
Solar Corona, and the Zodiacal Light, are 
especially valuable, embodying as they do 
the most recent observations and dis- 
coveries.' EXAiUNER. 



London, LONGMANS & CO. 



Works hi/ R. A. PiJOCTOR, B.A. 



SATUEX and its SYSTEM; C3ntaining Discussions of 

tlie Motions (real and apparent) and Telescopic Appearance of the 
Planet Saturn, its Satellites and Rings ; the Nature of the Rings ; 

the Great Inequality of Saturn and Jupiter; and the Habitability 
of Saturn. To which are appended Notes on Chaldaean Astronomy, 
Laplace's XeLuiar Theory, and the Habitability of the Moon; 
Annotated Tables : and Astronomical Vocabulary, AVith 14 Plates. 



Bvo. price 14s, 



' Mr. Proctor's new theoiy of the rings 
in definitely raises onr estimate of the 
marvellous nature of the phenomena tlie:r 

exhibit Mr, Proctor may fairly 

claim the title of the historian of Saturn. 
All that is known about the planet, and all 
that can be conjectured by a well-trained 
iiiathematical mind, is detailed at length 
in this Tolume.' Spectator, 

' A most valuable volume From 

it. more than from almost any other book 
with which we are acquainted, do we get 
an idea of the stupendous actual and 



potential enersies of our minds, and of 
the many-sided attacks made by them 
upon thiui^s unknown. How many in a 
thousand know as much of our earth a.< 
anybcdy may learn about Saturn in a day 
from the book before us? Mr. Proctou 
is happy in his subject, and equally happy 
in Ms treatment of it. The illustrations 
are second to none we have ever seen, and 
add greatly to the value of the book, the 
style of which is really a model of semi- 
special treatment of a scientific subject." 

EXA3nXER. 



A NEW STAR ATLAS, for the Library, the School, 

^nd the Observatory, in 12 Circular Maps (with 2 Index Plates). 
Intended as a Companion to ' Webb's Celestial Objects for Common 
Telescopes,' With an Introduction on the Study of the Stars, 

illustrated by 9 Diagrams. Crown 8vo. price 6s. 



' The small size of this excellent Atlas 
renders it quite capable of being carried 
in the pocket, and makes it, in conse- 
quence, very handy. The distortion in 
these map=. resulting from the necessity 
of representing a convex surface by a flat 
one. so that objects in the centre are of 
necessity on a much smaller scale than 
those near the circumference, is reduced 
to a minimum. The maus are twelve in 
iiumber. and are veiy clearly and admir- 
ably engi'aved : ther^? is a short introduc- 
tion, which will help the beginner very 
considerably ; and. on the whole, the work 
is one hkely to be useful both to the 
learner and the scientific astronomer." 
Educattoxal Tdies. 

•' The great difficulty in all celestial 
atlases is to get rid of the distortion con- 
sequent on the necessity of representing a 



spherical surface upon a flat one. Of 
course, in terrestrial maps the same diffi- 
culty exists, but in a much less degree, as 
the spaces on earth are so much smaller, 
in comparison with the amount of spheri- 
cal curvature, than those in the heavens. 
In many atlases, even in one as good as 
that pubhshed by the Useful Knowledge 
Society, the same space in the heavens 
occupies five times as much at the edge 
as in the centre of the map, and such a 
disproportion goes a long way to make 
the maps entirely useless. In the present 
Atlas this distortion is immensely re- 
duce! : biu its small and handy size is its 
great recommendaTion. The book is one 
for the pocket or the observatory, and 
contains in a small compass as much as 
many volumes tvv-ice its size.' 

Laxd and Water. 



London. LONGMANS & CO. 






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